Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
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×D724 | C2 | semidirect |
| 2. C2×#19153844 | C2 | semidirect |
| 3. #26041790 | C2 | semidirect |
| 4. #26041432 | C2 | semidirect |
| 5. #26041415 | C2 | semidirect |
| 6. #26041285 | C2 | semidirect |
| 7. #407×C181 | C2 | semidirect |
| 9. C2×#15668449 | C22 | semidirect |
| 16. C2×#15668438 | C22 | semidirect |
| 17. C2×D1448 | C22 | semidirect |
| 19. #19153795 | C22 | semidirect |
| 20. #19153790 | C22 | semidirect |
| 23. #19153775 | C22 | semidirect |
| 24. #19153738 | C22 | semidirect |
| 26. C2×M16×C181 | C22 | semidirect |
| 27. C22⋊C8×C181 | C22 | semidirect |
| 33. C2×Dic362 | C23 | semidirect |
| 40. C2×D724 | D4 | semidirect |
| 42. C2×D724 | C23 | semidirect |
| 48. C4⋊Dic181 | C23 | semidirect |
| 61. C2×C8×C181 | C23 | semidirect |
| 98. C22×C181 | AGL(1,ℤ/8) | semidirect |
| 117. C181 | #3003 | semidirect |
| 125. #407 | D181 | semidirect |
| 137. C2×M16 | C2×D181 | semidirect |
| 145. C22⋊C8 | C2×D181 | semidirect |
| 173. C2×C8 | C22×D181 | semidirect |
| 222. C22 | #19153844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D724 | 2 |
| C2×#19153844 | 2 |
| #26041790 | 2 |
| #26041432 | 2 |
| #26041415 | 2 |
| #26041285 | 2 |
| #407×C181 | 2 |
| #3003 | 181 |