Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×Dic724 | C2 | semidirect |
| 3. C2×#19153741 | C2 | semidirect |
| 4. #26041042 | C2 | semidirect |
| 57. C23×C181 | Q16 | semidirect |
| 92. C181 | #2001 | semidirect |
| 140. C23 | Dic724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| C2×#19153795 | 2 |
| C2×#19153741 | 2 |
| #26041042 | 2 |
| C2×C22⋊C8×C181 | 2 |
| #2001 | 181 |