Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic346 | C2 | semidirect |
| 2. #26011824 | C2 | semidirect |
| 4. #26011795 | C2 | semidirect |
| 5. #26011710 | C2 | semidirect |
| 6. #26011646 | C2 | semidirect |
| 8. #26011596 | C2 | semidirect |
| 9. #26011591 | C2 | semidirect |
| 10. #26011548 | C2 | semidirect |
| 131. C173 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011824 | 2 |
| #26011807 | 2 |
| #26011795 | 2 |
| #26011710 | 2 |
| #26011646 | 2 |
| #26011629 | 2 |
| #26011596 | 2 |
| #26011591 | 2 |
| #26011548 | 2 |
| #529×C173 | 2 |
| #3117 | 173 |