Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 44. #13063443 | Q16 | semidirect |
| 71. C173 | #1584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012541 | 2 |
| #26012540 | 2 |
| #26012355 | 2 |
| #26012341 | 2 |
| #13063443⋊C8 | 2 |
| #26011585 | 2 |
| #1584 | 173 |