Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 162 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. #26042331 | C2 | semidirect |
| 2. #26042329 | C2 | semidirect |
| 27. D181⋊C8 | Q8 | semidirect |
| 73. C181 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042331 | 2 |
| #26042329 | 2 |
| #26042286 | 2 |
| #26042283 | 2 |
| #26042244 | 2 |
| #26042238 | 2 |
| #26041835 | 2 |
| #2961 | 181 |