Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 150 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. #26012542 | C2 | semidirect |
| 2. #26012523 | C2 | semidirect |
| 3. #26012522 | C2 | semidirect |
| 4. #26012518 | C2 | semidirect |
| 5. #26012515 | C2 | semidirect |
| 6. #26012509 | C2 | semidirect |
| 7. #26012455 | C2 | semidirect |
| 8. #26012450 | C2 | semidirect |
| 111. C173 | #2968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012542 | 2 |
| #26012523 | 2 |
| #26012522 | 2 |
| #26012518 | 2 |
| #26012515 | 2 |
| #26012509 | 2 |
| #26012455 | 2 |
| #26012450 | 2 |
| #26012020 | 2 |
| #2968 | 173 |