Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 43. #13089678 | Q16 | semidirect |
| 63. C181 | #1723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041684 | 2 |
| #26041682 | 2 |
| #26041675 | 2 |
| #26041658 | 2 |
| #26041631 | 2 |
| #26041001 | 2 |
| #487×C181 | 2 |
| #1723 | 181 |