Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774452 | C2 | semidirect |
| 3. #31774231 | C2 | semidirect |
| 4. #31774178 | C2 | semidirect |
| 5. #31774177 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 8. #31774000 | C2 | semidirect |
| 9. #31773998 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #461×C271 | C2 | semidirect |
| 15. #22576160 | C22 | semidirect |
| 19. Q8×Dic271 | C22 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. C4⋊(C271⋊C8) | C22 | semidirect |
| 33. #22576084 | C22 | semidirect |
| 37. #22576070 | C22 | semidirect |
| 39. C4⋊Q8×C271 | C22 | semidirect |
| 41. C4⋊C8×C271 | C22 | semidirect |
| 42. #103×C271 | C22 | semidirect |
| 146. C271 | #3110 | semidirect |
| 154. #461 | D271 | semidirect |
| 164. C4⋊Q8 | C2×D271 | semidirect |
| 183. C4⋊C8 | C2×D271 | semidirect |
| 185. #103 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×D4×D271 | 2 |
| #31774231 | 2 |
| #31774178 | 2 |
| #31774177 | 2 |
| #31774099 | 2 |
| #31774046 | 2 |
| #31774000 | 2 |
| #31773998 | 2 |
| #31773953 | 2 |
| #461×C271 | 2 |
| #3110 | 271 |