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. #26011796 | C2 | semidirect |
| 7. #26011698 | C2 | semidirect |
| 8. C8×Dic346 | C2 | semidirect |
| 9. #26011583 | C2 | semidirect |
| 11. #487×C173 | C2 | semidirect |
| 115. C173 | #3364 | semidirect |
| 120. #487 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012216 | 2 |
| #26012215 | 2 |
| #26011847 | 2 |
| #26011796 | 2 |
| #26011768 | 2 |
| #26011716 | 2 |
| #26011698 | 2 |
| C8×Dic346 | 2 |
| #26011583 | 2 |
| C4×#14583815 | 2 |
| #487×C173 | 2 |
| #3364 | 173 |