Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041824 | C2 | semidirect |
| 2. C2×#19153778 | C2 | semidirect |
| 3. #26041592 | C2 | semidirect |
| 4. #26041558 | C2 | semidirect |
| 5. #26041473 | C2 | semidirect |
| 6. #26041415 | C2 | semidirect |
| 7. #26041412 | C2 | semidirect |
| 8. #26041361 | C2 | semidirect |
| 9. #26041359 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #480×C181 | C2 | semidirect |
| 17. #19153815 | C22 | semidirect |
| 18. #19153812 | C22 | semidirect |
| 22. D4×Dic181 | C22 | semidirect |
| 27. #19153778 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 40. #107×C181 | C22 | semidirect |
| 41. #102×C181 | C22 | semidirect |
| 92. D724 | #41 | semidirect |
| 99. C2×Dic181 | D8 | semidirect |
| 149. C181 | #3100 | semidirect |
| 154. #480 | D181 | semidirect |
| 184. #107 | C2×D181 | semidirect |
| 189. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| C2×#19153778 | 2 |
| #26041592 | 2 |
| #26041558 | 2 |
| #26041473 | 2 |
| #26041415 | 2 |
| #26041412 | 2 |
| #26041361 | 2 |
| #26041359 | 2 |
| #26041329 | 2 |
| #480×C181 | 2 |
| #3100 | 181 |