Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26041986 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041598 | C2 | semidirect |
| 5. #26041570 | C2 | semidirect |
| 6. #26041508 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041432 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. C2×#19153738 | C2 | semidirect |
| 11. C8×D4×C181 | C2 | semidirect |
| 15. C2×#15668438 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 19. #19153795 | C22 | semidirect |
| 24. C4×Dic362 | C22 | semidirect |
| 27. C2×C4⋊Dic181 | C22 | semidirect |
| 28. #19153748 | C22 | semidirect |
| 29. #19153748 | C22 | semidirect |
| 30. #19153741 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153738 | C22 | semidirect |
| 35. #19153738 | C22 | semidirect |
| 36. C22×C8×C181 | C22 | semidirect |
| 38. C4⋊C8×C181 | C22 | semidirect |
| 39. C22⋊C8×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 100. D4×C181 | SD16 | semidirect |
| 136. C181 | #3295 | semidirect |
| 147. C8×D4 | D181 | semidirect |
| 153. C22×C8 | C2×D181 | semidirect |
| 169. C4⋊C8 | C2×D181 | semidirect |
| 176. C22⋊C8 | C2×D181 | semidirect |
| 177. C4×C8 | C2×D181 | semidirect |
| 231. D4 | #15668438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041986 | 2 |
| D4×D724 | 2 |
| #26041626 | 2 |
| #26041598 | 2 |
| #26041570 | 2 |
| #26041508 | 2 |
| #26041480 | 2 |
| #26041432 | 2 |
| C4×#15668438 | 2 |
| C2×#19153738 | 2 |
| C8×D4×C181 | 2 |
| #3295 | 181 |