Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
150 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 150 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 |
|---|---|---|
| 56. C8×C181 | Q16 | semidirect |
| 70. C181 | #1672 | semidirect |
| 127. C8 | #15668439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041677 | 2 |
| #26041574 | 2 |
| #26041489 | 2 |
| #26041030 | 2 |
| #26041027 | 2 |
| #26041024 | 2 |
| C8×Q8×C181 | 2 |
| #1672 | 181 |