Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #31774372 | C2 | semidirect |
| 3. #31774371 | C2 | semidirect |
| 4. #31774006 | C2 | semidirect |
| 5. #31773977 | C2 | semidirect |
| 6. #31773933 | C2 | semidirect |
| 7. #31773903 | C2 | semidirect |
| 8. #31773855 | C2 | semidirect |
| 9. #418×C271 | C2 | semidirect |
| 11. C2×#16864639 | C4 | semidirect |
| 17. D4×Dic271 | C22 | semidirect |
| 18. #22576122 | C22 | semidirect |
| 23. #22576093 | C22 | semidirect |
| 24. #22576091 | C22 | semidirect |
| 25. #22576082 | C22 | semidirect |
| 26. #22576070 | C22 | semidirect |
| 27. C8×Dic271 | C22 | semidirect |
| 31. #102×C271 | C22 | semidirect |
| 35. C2×D1084 | C2×C4 | semidirect |
| 39. #16864639 | C2×C4 | semidirect |
| 40. #16864639 | C2×C4 | semidirect |
| 41. C2×C271⋊C8 | C2×C4 | semidirect |
| 55. C2×D4×C271 | C2×C4 | semidirect |
| 108. C271 | #2948 | semidirect |
| 117. #418 | D271 | semidirect |
| 138. #102 | C2×D271 | semidirect |
| 149. C2×D4 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864639 | 2 |
| #31774372 | 2 |
| #31774371 | 2 |
| #31774006 | 2 |
| #31773977 | 2 |
| #31773933 | 2 |
| #31773903 | 2 |
| #31773855 | 2 |
| #418×C271 | 2 |
| #2948 | 271 |