Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
394 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 144 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. #26012523 | C2 | semidirect |
| 2. #26012522 | C2 | semidirect |
| 3. #26012521 | C2 | semidirect |
| 4. #26012520 | C2 | semidirect |
| 5. #26012512 | C2 | semidirect |
| 6. #26012511 | C2 | semidirect |
| 7. #26012465 | C2 | semidirect |
| 8. #26012464 | C2 | semidirect |
| 123. C173 | #2980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012523 | 2 |
| #26012522 | 2 |
| #26012521 | 2 |
| #26012520 | 2 |
| #26012512 | 2 |
| #26012511 | 2 |
| #26012465 | 2 |
| #26012464 | 2 |
| #26012036 | 2 |
| #2980 | 173 |