Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041950 | C2 | semidirect |
| 2. #26041944 | C2 | semidirect |
| 3. #26041627 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041558 | C2 | semidirect |
| 6. #26041475 | C2 | semidirect |
| 7. #26041473 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 9. #26041361 | C2 | semidirect |
| 10. C4×#15668434 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 78. Dic362 | D8 | semidirect |
| 84. D724 | #41 | semidirect |
| 131. C181 | #3358 | semidirect |
| 138. #474 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041950 | 2 |
| #26041944 | 2 |
| #26041627 | 2 |
| #26041624 | 2 |
| #26041558 | 2 |
| #26041475 | 2 |
| #26041473 | 2 |
| #26041403 | 2 |
| #26041361 | 2 |
| C4×#15668434 | 2 |
| #474×C181 | 2 |
| #3358 | 181 |