Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26011534 | C2 | semidirect |
| 2. C2×#19149606 | C2 | semidirect |
| 3. #26011492 | C2 | semidirect |
| 4. C2×#19149596 | C2 | semidirect |
| 5. #26011394 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 32. #14583810 | D4 | semidirect |
| 130. C173 | #2037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011534 | 2 |
| C2×#19149606 | 2 |
| #26011492 | 2 |
| C2×#19149596 | 2 |
| #26011394 | 2 |
| #26011250 | 2 |
| #535×C173 | 2 |
| #2037 | 173 |