Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
152 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 70 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. #26042200 | C2 | semidirect |
| 3. #26042168 | C2 | semidirect |
| 57. C181 | #2163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042200 | 2 |
| C22⋊#15668452 | 2 |
| #26042168 | 2 |
| C2×C8×Dic181 | 2 |
| #2163 | 181 |