Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #26012097 | C2 | semidirect |
| 2. #26011868 | C2 | semidirect |
| 3. #26011857 | C2 | semidirect |
| 4. #26011745 | C2 | semidirect |
| 5. #26011728 | C2 | semidirect |
| 6. #26011602 | C2 | semidirect |
| 7. #26011573 | C2 | semidirect |
| 8. #26011445 | C2 | semidirect |
| 9. #499×C173 | C2 | semidirect |
| 84. C173 | #3176 | semidirect |
| 87. #499 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012097 | 2 |
| #26011868 | 2 |
| #26011857 | 2 |
| #26011745 | 2 |
| #26011728 | 2 |
| #26011602 | 2 |
| #26011573 | 2 |
| #26011445 | 2 |
| #499×C173 | 2 |
| #3176 | 173 |