Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 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. #26041682 | C2 | semidirect |
| 4. #26041026 | C2 | semidirect |
| 5. Q8⋊#13089678 | C2 | semidirect |
| 7. #462×C181 | C2 | semidirect |
| 55. D724 | Q16 | semidirect |
| 92. C181 | #1649 | semidirect |
| 97. #462 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D724 | 2 |
| #26041682 | 2 |
| #26041556 | 2 |
| #26041026 | 2 |
| Q8⋊#13089678 | 2 |
| #26041006 | 2 |
| #462×C181 | 2 |
| #1649 | 181 |