Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041586 | C2 | semidirect |
| 3. #26041583 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 7. #26041486 | C2 | semidirect |
| 94. C181 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041891 | 2 |
| #26041586 | 2 |
| #26041583 | 2 |
| #26041535 | 2 |
| #26041518 | 2 |
| #26041489 | 2 |
| #26041486 | 2 |
| #26041306 | 2 |
| #541×C181 | 2 |
| #3261 | 181 |