Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
356 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 177 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. #26041409 | C2 | semidirect |
| 3. #26041406 | C2 | semidirect |
| 78. C181 | #2983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic362 | 2 |
| #26041409 | 2 |
| #26041406 | 2 |
| #26041333 | 2 |
| #26041332 | 2 |
| #431×C181 | 2 |
| #2983 | 181 |