Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
206 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 39. Q8×C181 | Q16 | semidirect |
| 55. C181 | #1633 | semidirect |
| 92. Q8 | #15668439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041658 | 2 |
| #26041574 | 2 |
| #26041028 | 2 |
| Q8⋊#13089678 | 2 |
| Q82×C181 | 2 |
| #1633 | 181 |