Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19149709 | C2 | semidirect |
| 2. D4×Dic346 | C2 | semidirect |
| 3. #26011870 | C2 | semidirect |
| 4. #26011747 | C2 | semidirect |
| 5. #26011698 | C2 | semidirect |
| 6. #26011696 | C2 | semidirect |
| 7. #26011653 | C2 | semidirect |
| 8. #26011646 | C2 | semidirect |
| 9. C4×#14583814 | C2 | semidirect |
| 10. #26011569 | C2 | semidirect |
| 52. #14583814 | D4 | semidirect |
| 123. C4×C173 | #137 | semidirect |
| 134. C173 | #3276 | semidirect |
| 261. C4 | #19149709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| D4×Dic346 | 2 |
| #26011870 | 2 |
| #26011747 | 2 |
| #26011698 | 2 |
| #26011696 | 2 |
| #26011653 | 2 |
| #26011646 | 2 |
| C4×#14583814 | 2 |
| #26011569 | 2 |
| #547×C173 | 2 |
| #3276 | 173 |