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. #26041587 | C2 | semidirect |
| 5. #26041490 | C2 | semidirect |
| 65. C181 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041891 | 2 |
| #26041587 | 2 |
| #26041537 | 2 |
| #26041520 | 2 |
| #26041490 | 2 |
| #424×C181 | 2 |
| #3261 | 181 |