Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041891 | C2 | semidirect |
| 3. #26041673 | C2 | semidirect |
| 4. #26041652 | C2 | semidirect |
| 5. #26041644 | C2 | semidirect |
| 6. #26041634 | C2 | semidirect |
| 7. #26041502 | C2 | semidirect |
| 8. #26041480 | C2 | semidirect |
| 9. #26041443 | C2 | semidirect |
| 10. #26041432 | C2 | semidirect |
| 11. #433×C181 | C2 | semidirect |
| 14. C2×Dic724 | C22 | semidirect |
| 17. C2×#15668438 | C22 | semidirect |
| 18. #19153816 | C22 | semidirect |
| 22. #19153808 | C22 | semidirect |
| 29. C4×Dic362 | C22 | semidirect |
| 30. #19153741 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 35. C4⋊C8×C181 | C22 | semidirect |
| 37. #97×C181 | C22 | semidirect |
| 38. C4×C8×C181 | C22 | semidirect |
| 122. C181 | #3222 | semidirect |
| 134. #433 | D181 | semidirect |
| 154. C4⋊C8 | C2×D181 | semidirect |
| 160. #97 | C2×D181 | semidirect |
| 161. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041891 | 2 |
| #26041848 | 2 |
| #26041673 | 2 |
| #26041652 | 2 |
| #26041644 | 2 |
| #26041634 | 2 |
| #26041502 | 2 |
| #26041480 | 2 |
| #26041443 | 2 |
| #26041432 | 2 |
| #433×C181 | 2 |
| #3222 | 181 |