Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153822 | C2 | semidirect |
| 2. #26041846 | C2 | semidirect |
| 3. #26041529 | C2 | semidirect |
| 4. #26041512 | C2 | semidirect |
| 5. #26041317 | C2 | semidirect |
| 6. #26041284 | C2 | semidirect |
| 7. C22×D8×C181 | C2 | semidirect |
| 11. C2×#15668432 | C22 | semidirect |
| 12. C2×C8×D181 | C22 | semidirect |
| 15. #19153787 | C22 | semidirect |
| 18. #19153750 | C22 | semidirect |
| 19. #19153748 | C22 | semidirect |
| 20. #19153737 | C22 | semidirect |
| 49. C2×C8×C181 | D4 | semidirect |
| 93. C181 | #3058 | semidirect |
| 95. C22×D8 | D181 | semidirect |
| 139. 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×#19153822 | 2 |
| #26041846 | 2 |
| #26041529 | 2 |
| #26041512 | 2 |
| #26041317 | 2 |
| #26041284 | 2 |
| C22×D8×C181 | 2 |
| #3058 | 181 |