Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D1084 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. #31774408 | C2 | semidirect |
| 4. #31774050 | C2 | semidirect |
| 5. #31774033 | C2 | semidirect |
| 6. #31773903 | C2 | semidirect |
| 7. #407×C271 | C2 | semidirect |
| 9. C2×#16864654 | C22 | semidirect |
| 16. C2×#16864643 | C22 | semidirect |
| 17. C2×D2168 | C22 | semidirect |
| 19. #22576139 | C22 | semidirect |
| 20. #22576134 | C22 | semidirect |
| 23. #22576119 | C22 | semidirect |
| 24. #22576082 | C22 | semidirect |
| 26. C2×M16×C271 | C22 | semidirect |
| 27. C22⋊C8×C271 | C22 | semidirect |
| 33. C2×Dic542 | C23 | semidirect |
| 40. C2×D1084 | D4 | semidirect |
| 42. C2×D1084 | C23 | semidirect |
| 48. C4⋊Dic271 | C23 | semidirect |
| 61. C2×C8×C271 | C23 | semidirect |
| 98. C22×C271 | AGL(1,ℤ/8) | semidirect |
| 117. C271 | #3003 | semidirect |
| 125. #407 | D271 | semidirect |
| 137. C2×M16 | C2×D271 | semidirect |
| 145. C22⋊C8 | C2×D271 | semidirect |
| 173. C2×C8 | C22×D271 | semidirect |
| 222. C22 | #22576188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D1084 | 2 |
| C2×#22576188 | 2 |
| #31774408 | 2 |
| #31774050 | 2 |
| #31774033 | 2 |
| #31773903 | 2 |
| #407×C271 | 2 |
| #3003 | 271 |