Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×M16×D271 | C2 | semidirect |
| 3. C2×#22576136 | C2 | semidirect |
| 4. #31774152 | C2 | semidirect |
| 5. #31774140 | C2 | semidirect |
| 6. #31774135 | C2 | semidirect |
| 7. #31774123 | C2 | semidirect |
| 8. #31773939 | C2 | semidirect |
| 9. #31773906 | C2 | semidirect |
| 10. #31773898 | C2 | semidirect |
| 11. C2×#137×C271 | C2 | semidirect |
| 33. #22576094 | C22 | semidirect |
| 34. #22576092 | C22 | semidirect |
| 35. #22576084 | C22 | semidirect |
| 36. #22576084 | C22 | semidirect |
| 37. #22576084 | C22 | semidirect |
| 38. #22576081 | C22 | semidirect |
| 42. C2×Q16×C271 | C22 | semidirect |
| 43. C2×SD16×C271 | C22 | semidirect |
| 90. M16×C271 | D4 | semidirect |
| 145. C2×D271 | #137 | semidirect |
| 163. C271 | #3056 | semidirect |
| 165. C2×#137 | D271 | semidirect |
| 180. C2×Q16 | C2×D271 | semidirect |
| 181. C2×SD16 | C2×D271 | semidirect |
| 236. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D271 | 2 |
| #31774404 | 2 |
| C2×#22576136 | 2 |
| #31774152 | 2 |
| #31774140 | 2 |
| #31774135 | 2 |
| #31774123 | 2 |
| #31773939 | 2 |
| #31773906 | 2 |
| #31773898 | 2 |
| C2×#137×C271 | 2 |
| #3056 | 271 |