Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×D1448 | C2 | semidirect |
| 2. C2×#19153822 | C2 | semidirect |
| 3. #26041848 | C2 | semidirect |
| 4. #26041533 | C2 | semidirect |
| 5. #26041516 | C2 | semidirect |
| 6. #26041283 | C2 | semidirect |
| 7. #427×C181 | C2 | semidirect |
| 15. C2×#15668432 | C22 | semidirect |
| 16. C2×C8×D181 | C22 | semidirect |
| 19. #19153791 | C22 | semidirect |
| 21. #19153736 | C22 | semidirect |
| 24. #107×C181 | C22 | semidirect |
| 25. #106×C181 | C22 | semidirect |
| 46. C2×C8×C181 | D4 | semidirect |
| 93. C181 | #3058 | semidirect |
| 100. #427 | D181 | semidirect |
| 117. #107 | C2×D181 | semidirect |
| 118. #106 | C2×D181 | semidirect |
| 139. C2×C8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1448 | 2 |
| C2×#19153822 | 2 |
| #26041848 | 2 |
| #26041533 | 2 |
| #26041516 | 2 |
| #26041283 | 2 |
| #427×C181 | 2 |
| #3058 | 181 |