Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26012070 | C2 | semidirect |
| 2. #26011823 | C2 | semidirect |
| 3. #26011808 | C2 | semidirect |
| 4. #26011749 | C2 | semidirect |
| 5. #26011718 | C2 | semidirect |
| 6. #26011654 | C2 | semidirect |
| 7. #26011633 | C2 | semidirect |
| 8. #26011459 | C2 | semidirect |
| 9. #469×C173 | C2 | semidirect |
| 117. C173 | #3204 | semidirect |
| 123. #469 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012070 | 2 |
| #26011823 | 2 |
| #26011808 | 2 |
| #26011749 | 2 |
| #26011718 | 2 |
| #26011654 | 2 |
| #26011633 | 2 |
| #26011459 | 2 |
| #469×C173 | 2 |
| #3204 | 173 |