Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 2. #26042142 | C2 | semidirect |
| 3. #26042140 | C2 | semidirect |
| 60. C181 | #1568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042301 | 2 |
| #26042142 | 2 |
| #26042140 | 2 |
| C4×C8×D181 | 2 |
| #1568 | 181 |