Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
152 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 47. #13063436 | Q16 | semidirect |
| 72. C173 | #1694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011894 | 2 |
| #26011701 | 2 |
| #26011622 | 2 |
| #26011241 | 2 |
| #26011238 | 2 |
| #26011237 | 2 |
| #462×C173 | 2 |
| #1694 | 173 |