Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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×C22⋊#13063436 | C2 | semidirect |
| 3. #26011227 | C2 | semidirect |
| 4. #26011224 | C2 | semidirect |
| 5. #381×C173 | C2 | semidirect |
| 6. C2×#14583826 | C4 | semidirect |
| 9. #19149658 | C4 | semidirect |
| 11. #19149653 | C4 | semidirect |
| 16. #19149638 | C4 | semidirect |
| 111. C173 | #1516 | semidirect |
| 115. #381 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012002 | 2 |
| C2×C22⋊#13063436 | 2 |
| #26011227 | 2 |
| #26011224 | 2 |
| #381×C173 | 2 |
| #1516 | 173 |