Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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. #26011791 | C2 | semidirect |
| 3. #26011788 | C2 | semidirect |
| 4. #26011742 | C2 | semidirect |
| 5. #26011725 | C2 | semidirect |
| 6. #26011686 | C2 | semidirect |
| 7. #26011683 | C2 | semidirect |
| 8. #26011518 | C2 | semidirect |
| 9. #540×C173 | C2 | semidirect |
| 106. C173 | #3259 | semidirect |
| 109. #540 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012096 | 2 |
| #26011791 | 2 |
| #26011788 | 2 |
| #26011742 | 2 |
| #26011725 | 2 |
| #26011686 | 2 |
| #26011683 | 2 |
| #26011518 | 2 |
| #540×C173 | 2 |
| #3259 | 173 |