Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31774700 | C2 | semidirect |
| 2. #31774699 | C2 | semidirect |
| 3. #31774272 | C2 | semidirect |
| 4. #31774167 | C2 | semidirect |
| 5. #31774165 | C2 | semidirect |
| 6. #31774164 | C2 | semidirect |
| 7. #31774065 | C2 | semidirect |
| 8. #31774063 | C2 | semidirect |
| 9. #31774014 | C2 | semidirect |
| 10. #31774012 | C2 | semidirect |
| 11. #576×C271 | C2 | semidirect |
| 12. #22576206 | C22 | semidirect |
| 15. #22576186 | C22 | semidirect |
| 17. #22576185 | C22 | semidirect |
| 18. #22576185 | C22 | semidirect |
| 22. C2×D2168 | C22 | semidirect |
| 24. C2×#16864639 | C22 | semidirect |
| 26. #22576167 | C22 | semidirect |
| 27. #22576166 | C22 | semidirect |
| 28. #22576156 | C22 | semidirect |
| 29. #22576096 | C22 | semidirect |
| 30. #22576095 | C22 | semidirect |
| 31. #22576087 | C22 | semidirect |
| 32. #22576087 | C22 | semidirect |
| 33. #22576086 | C22 | semidirect |
| 34. #22576077 | C22 | semidirect |
| 35. #22576076 | C22 | semidirect |
| 36. C8×Dic271 | C22 | semidirect |
| 37. H(5,𝔽2)×C271 | C22 | semidirect |
| 39. AGL(1,ℤ/8)×C271 | C22 | semidirect |
| 43. C2×D8×C271 | C22 | semidirect |
| 44. #131×C271 | C22 | semidirect |
| 53. #16864644 | D4 | semidirect |
| 55. #16864642 | D4 | semidirect |
| 58. #16864641 | D4 | semidirect |
| 66. #16864639 | D4 | semidirect |
| 83. Q16×C271 | D4 | semidirect |
| 85. SD16×C271 | D4 | semidirect |
| 89. D8×C271 | D4 | semidirect |
| 153. C271 | #3292 | semidirect |
| 157. #576 | D271 | semidirect |
| 167. H(5,𝔽2) | C2×D271 | semidirect |
| 175. AGL(1,ℤ/8) | C2×D271 | semidirect |
| 186. C2×D8 | C2×D271 | semidirect |
| 189. #131 | C2×D271 | semidirect |
| 216. Q16 | C22⋊D271 | semidirect |
| 223. SD16 | C22⋊D271 | semidirect |
| 235. D8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774700 | 2 |
| #31774699 | 2 |
| #31774272 | 2 |
| #31774167 | 2 |
| #31774165 | 2 |
| #31774164 | 2 |
| #31774065 | 2 |
| #31774063 | 2 |
| #31774014 | 2 |
| #31774012 | 2 |
| #576×C271 | 2 |
| #3292 | 271 |