Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
280 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 35. C2×#13089678 | Q8 | semidirect |
| 51. C2×C8×C181 | Q8 | semidirect |
| 108. C181 | #1985 | semidirect |
| 153. C2×C8 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic362 | 2 |
| C2×#19153745 | 2 |
| C2×#19153726 | 2 |
| #26041034 | 2 |
| #26041033 | 2 |
| #336×C181 | 2 |
| #1985 | 181 |