Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
964 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 964 conjugacy classes of subgroups — too many to draw. Only its 553 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. Q8×Dic362 | C2 | semidirect |
| 2. #26042008 | C2 | semidirect |
| 3. #26042005 | C2 | semidirect |
| 35. C2×Q8×C181 | Q8 | semidirect |
| 70. C181 | #3502 | semidirect |
| 98. C2×Q8 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| #26042008 | 2 |
| #26042005 | 2 |
| #26041910 | 2 |
| #26041836 | 2 |
| #26041757 | 2 |
| C2×C4×Q8×C181 | 2 |
| #3502 | 181 |