Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 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. #26041387 | C2 | semidirect |
| 4. C4×Dic724 | C2 | semidirect |
| 9. C2×Dic724 | C4 | semidirect |
| 72. C181 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| #26041756 | 2 |
| #26041387 | 2 |
| C4×Dic724 | 2 |
| #26041317 | 2 |
| #26041289 | 2 |
| #405×C181 | 2 |
| #2950 | 181 |