Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
238 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 1. #26012514 | C2 | semidirect |
| 2. #26012346 | C2 | semidirect |
| 57. C173 | #1536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012514 | 2 |
| #26012346 | 2 |
| #26012039 | 2 |
| #1536 | 173 |