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 |
|---|---|---|
| 2. C2×C4×Dic346 | C2 | semidirect |
| 3. #26011827 | C2 | semidirect |
| 5. #26011799 | C2 | semidirect |
| 6. #26011714 | C2 | semidirect |
| 7. #26011649 | C2 | semidirect |
| 9. #26011599 | C2 | semidirect |
| 10. #26011593 | C2 | semidirect |
| 11. #432×C173 | C2 | semidirect |
| 131. C173 | #3117 | semidirect |
| 143. #432 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| C2×C4×Dic346 | 2 |
| #26011827 | 2 |
| #26011810 | 2 |
| #26011799 | 2 |
| #26011714 | 2 |
| #26011649 | 2 |
| #26011632 | 2 |
| #26011599 | 2 |
| #26011593 | 2 |
| #432×C173 | 2 |
| #3117 | 173 |