Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012096 | C2 | semidirect |
| 2. #26012067 | C2 | semidirect |
| 3. #26011880 | C2 | semidirect |
| 4. #26011864 | C2 | semidirect |
| 5. #26011860 | C2 | semidirect |
| 6. #26011846 | C2 | semidirect |
| 7. #26011707 | C2 | semidirect |
| 8. #26011697 | C2 | semidirect |
| 9. #26011638 | C2 | semidirect |
| 10. #26011632 | C2 | semidirect |
| 11. #433×C173 | C2 | semidirect |
| 120. C173 | #3221 | semidirect |
| 132. #433 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012096 | 2 |
| #26012067 | 2 |
| #26011880 | 2 |
| #26011864 | 2 |
| #26011860 | 2 |
| #26011846 | 2 |
| #26011707 | 2 |
| #26011697 | 2 |
| #26011638 | 2 |
| #26011632 | 2 |
| #433×C173 | 2 |
| #3221 | 173 |