Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 3. #26012348 | C2 | semidirect |
| 4. #26012348 | C2 | semidirect |
| 85. C173 | #1528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012514 | 2 |
| C4×#14583836 | 2 |
| #26012348 | 2 |
| #125×D173 | 2 |
| #1528 | 173 |