Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26012046 | C2 | semidirect |
| 3. #26011801 | C2 | semidirect |
| 4. #26011793 | C2 | semidirect |
| 5. #26011783 | C2 | semidirect |
| 6. #26011777 | C2 | semidirect |
| 7. #26011771 | C2 | semidirect |
| 8. #26011526 | C2 | semidirect |
| 9. C4⋊C8×D173 | C2 | semidirect |
| 11. #476×C173 | C2 | semidirect |
| 44. #14583825 | Q8 | semidirect |
| 134. C173 | #3076 | semidirect |
| 141. #476 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| C4×#14583825 | 2 |
| #26011801 | 2 |
| #26011793 | 2 |
| #26011783 | 2 |
| #26011777 | 2 |
| #26011771 | 2 |
| #26011526 | 2 |
| C4⋊C8×D173 | 2 |
| #26011484 | 2 |
| #476×C173 | 2 |
| #3076 | 173 |