Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19153846 | C2 | semidirect |
| 4. C2×#19153781 | C2 | semidirect |
| 5. #26041504 | C2 | semidirect |
| 6. #26041500 | C2 | semidirect |
| 7. #26041488 | C2 | semidirect |
| 8. #26041478 | C2 | semidirect |
| 9. #26041302 | C2 | semidirect |
| 10. #26041278 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 49. C2×Dic362 | D4 | semidirect |
| 150. Dic181 | #137 | semidirect |
| 157. C181 | #3037 | semidirect |
| 169. #417 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153846 | 2 |
| #26041825 | 2 |
| C2×#19153781 | 2 |
| #26041504 | 2 |
| #26041500 | 2 |
| #26041488 | 2 |
| #26041478 | 2 |
| #26041302 | 2 |
| #26041278 | 2 |
| #417×C181 | 2 |
| #3037 | 181 |