Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#19153849 | C2 | semidirect |
| 2. C2×#19153844 | C2 | semidirect |
| 3. C2×#19153838 | C2 | semidirect |
| 4. C22×#15668438 | C2 | semidirect |
| 5. #26041855 | C2 | semidirect |
| 6. #26041848 | C2 | semidirect |
| 7. #26041673 | C2 | semidirect |
| 8. #26041668 | C2 | semidirect |
| 9. #26041663 | C2 | semidirect |
| 10. #26041652 | C2 | semidirect |
| 11. #405×C181 | C2 | semidirect |
| 19. C2×Dic724 | C22 | semidirect |
| 20. C2×Dic724 | C22 | semidirect |
| 25. C2×#15668438 | C22 | semidirect |
| 26. C2×#15668438 | C22 | semidirect |
| 27. C2×#15668438 | C22 | semidirect |
| 29. C2×D1448 | C22 | semidirect |
| 30. #19153816 | C22 | semidirect |
| 33. #19153804 | C22 | semidirect |
| 41. #97×C181 | C22 | semidirect |
| 42. C4×C8×C181 | C22 | semidirect |
| 80. M16×C181 | D4 | semidirect |
| 81. C2×C8×C181 | D4 | semidirect |
| 148. C181 | #3154 | semidirect |
| 160. #405 | D181 | semidirect |
| 190. #97 | C2×D181 | semidirect |
| 191. C4×C8 | C2×D181 | semidirect |
| 226. M16 | D724 | semidirect |
| 227. C2×C8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153844 | 2 |
| C2×#19153838 | 2 |
| C22×#15668438 | 2 |
| #26041855 | 2 |
| #26041848 | 2 |
| #26041673 | 2 |
| #26041668 | 2 |
| #26041663 | 2 |
| #26041652 | 2 |
| #405×C181 | 2 |
| #3154 | 181 |