Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
320 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 53. Q16×C181 | Q8 | semidirect |
| 90. C181 | #3390 | semidirect |
| 129. Q16 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042005 | 2 |
| #26041687 | 2 |
| #26041681 | 2 |
| #26041588 | 2 |
| #26041586 | 2 |
| #26041572 | 2 |
| #26041409 | 2 |
| #26041386 | 2 |
| C4×Q16×C181 | 2 |
| #3390 | 181 |