Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 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. #26012211 | C2 | semidirect |
| 2. D4×Dic346 | C2 | semidirect |
| 3. #26011849 | C2 | semidirect |
| 4. #26011842 | C2 | semidirect |
| 5. #26011785 | C2 | semidirect |
| 6. #26011771 | C2 | semidirect |
| 8. #26011696 | C2 | semidirect |
| 9. #26011621 | C2 | semidirect |
| 10. #26011588 | C2 | semidirect |
| 122. C173 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012211 | 2 |
| D4×Dic346 | 2 |
| #26011849 | 2 |
| #26011842 | 2 |
| #26011785 | 2 |
| #26011771 | 2 |
| #26011704 | 2 |
| #26011696 | 2 |
| #26011621 | 2 |
| #26011588 | 2 |
| C4×D8×C173 | 2 |
| #3367 | 173 |