Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26042077 | C2 | semidirect |
| 2. C2×#19153842 | C2 | semidirect |
| 3. #26041296 | C2 | semidirect |
| 4. #26041284 | C2 | semidirect |
| 5. #26041252 | C2 | semidirect |
| 6. #26041049 | C2 | semidirect |
| 7. #535×C181 | C2 | semidirect |
| 35. C2×Dic362 | D4 | semidirect |
| 36. C2×D724 | D4 | semidirect |
| 48. #15668433 | D4 | semidirect |
| 50. C2×#13089678 | D4 | semidirect |
| 142. C181 | #2008 | semidirect |
| 146. #535 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| C2×#19153842 | 2 |
| #26041296 | 2 |
| #26041284 | 2 |
| #26041252 | 2 |
| #26041049 | 2 |
| #535×C181 | 2 |
| #2008 | 181 |