Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
290 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 23. C2×Dic362 | Q8 | semidirect |
| 83. C181 | #2024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153816 | 2 |
| C2×#19153741 | 2 |
| #26041185 | 2 |
| #26041042 | 2 |
| #336×C181 | 2 |
| #2024 | 181 |