Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #26041373 | C2 | semidirect |
| 4. #26041106 | C2 | semidirect |
| 5. #26041084 | C2 | semidirect |
| 6. C16×Dic181 | C2 | semidirect |
| 11. #19153760 | C4 | semidirect |
| 23. Dic724 | C2×C4 | semidirect |
| 30. #15668424 | C2×C4 | semidirect |
| 62. Dic181 | SD32 | semidirect |
| 67. C181 | C4×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153760 | 2 |
| #26041373 | 2 |
| D8×Dic181 | 2 |
| #26041106 | 2 |
| #26041084 | 2 |
| C16×Dic181 | 2 |
| #357×C181 | 2 |
| C4×SD32 | 181 |