Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153842 | C2 | semidirect |
| 2. C2×#19153838 | C2 | semidirect |
| 3. #26041846 | C2 | semidirect |
| 4. #26041667 | C2 | semidirect |
| 5. #26041662 | C2 | semidirect |
| 6. #26041654 | C2 | semidirect |
| 7. #26041234 | C2 | semidirect |
| 8. C22×D8×C181 | C2 | semidirect |
| 12. C2×Dic724 | C22 | semidirect |
| 13. C2×#15668438 | C22 | semidirect |
| 14. C2×#15668437 | C22 | semidirect |
| 15. C2×D1448 | C22 | semidirect |
| 16. C2×#15668434 | C22 | semidirect |
| 18. #19153812 | C22 | semidirect |
| 19. #19153803 | C22 | semidirect |
| 23. #19153726 | C22 | semidirect |
| 24. C8×Dic181 | C22 | semidirect |
| 42. #15668433 | D4 | semidirect |
| 56. C2×C8×C181 | D4 | semidirect |
| 101. C181 | #3155 | semidirect |
| 105. C22×D8 | D181 | semidirect |
| 154. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| C2×#19153838 | 2 |
| #26041846 | 2 |
| #26041667 | 2 |
| #26041662 | 2 |
| #26041654 | 2 |
| #26041234 | 2 |
| C22×D8×C181 | 2 |
| #3155 | 181 |