Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
588 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 82 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. #26042277 | C2 | semidirect |
| 2. #26042271 | C2 | semidirect |
| 3. #26042265 | C2 | semidirect |
| 4. #26042258 | C2 | semidirect |
| 6. D181⋊M16 | C22 | semidirect |
| 7. #19153895 | C22 | semidirect |
| 16. C2×#15668449 | C4 | semidirect |
| 19. C2×#15668448 | C4 | semidirect |
| 24. C2×D4×D181 | C4 | semidirect |
| 26. C22×D4×C181 | C4 | semidirect |
| 151. C181 | #1795 | semidirect |
| 170. C22×D4 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042277 | 2 |
| #26042271 | 2 |
| #26042265 | 2 |
| #26042258 | 2 |
| C2×#19153861 | 2 |
| #1795 | 181 |