Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26041675 | C2 | semidirect |
| 2. #26041659 | C2 | semidirect |
| 3. #26041629 | C2 | semidirect |
| 6. #26041001 | C2 | semidirect |
| 68. C181 | #1720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041675 | 2 |
| #26041659 | 2 |
| #26041629 | 2 |
| #26041625 | 2 |
| #26041001 | 2 |
| #486×C181 | 2 |
| #1720 | 181 |