Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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. #26042250 | C2 | semidirect |
| 2. D181⋊(C22⋊C8) | C2 | semidirect |
| 3. #26042123 | C2 | semidirect |
| 99. C181 | #1471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042250 | 2 |
| D181⋊(C22⋊C8) | 2 |
| #26042123 | 2 |
| C2×#19153791 | 2 |
| #1471 | 181 |