Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
256 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 68 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. #26042297 | C2 | semidirect |
| 2. D181⋊(C4⋊C8) | C2 | semidirect |
| 3. #26042138 | C2 | semidirect |
| 4. #26042137 | C2 | semidirect |
| 104. C181 | #1540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042297 | 2 |
| D181⋊(C4⋊C8) | 2 |
| #26042138 | 2 |
| #26042137 | 2 |
| #26041826 | 2 |
| #1540 | 181 |