Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
190 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #13089685⋊C8 | C2 | semidirect |
| 4. #13089685⋊C8 | C2 | semidirect |
| 5. #26042120 | C2 | semidirect |
| 6. C8×#13089685 | C2 | semidirect |
| 73. C181 | #1453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042297 | 2 |
| C4×#15668459 | 2 |
| #13089685⋊C8 | 2 |
| #26042120 | 2 |
| C8×#13089685 | 2 |
| #26041331 | 2 |
| #1453 | 181 |