Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012216 | C2 | semidirect |
| 4. #26011843 | C2 | semidirect |
| 5. #26011797 | C2 | semidirect |
| 7. #26011702 | C2 | semidirect |
| 8. #26011615 | C2 | semidirect |
| 9. #26011585 | C2 | semidirect |
| 115. C173 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012216 | 2 |
| #26012211 | 2 |
| #26011844 | 2 |
| #26011843 | 2 |
| #26011797 | 2 |
| #26011712 | 2 |
| #26011702 | 2 |
| #26011615 | 2 |
| #26011585 | 2 |
| C4×#14583814 | 2 |
| #474×C173 | 2 |
| #3364 | 173 |