Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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. C2×#19149702 | C2 | semidirect |
| 2. #26012042 | C2 | semidirect |
| 3. C4×#14583827 | C2 | semidirect |
| 4. #26011715 | C2 | semidirect |
| 5. #26011709 | C2 | semidirect |
| 6. #26011693 | C2 | semidirect |
| 7. #26011691 | C2 | semidirect |
| 8. #26011687 | C2 | semidirect |
| 9. C4⋊C8×D173 | C2 | semidirect |
| 10. #26011486 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 47. #14583827 | D4 | semidirect |
| 137. C4×C173 | #135 | semidirect |
| 150. C173 | #3035 | semidirect |
| 157. #462 | D173 | semidirect |
| 292. C4 | #19149702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| #26012042 | 2 |
| C4×#14583827 | 2 |
| #26011715 | 2 |
| #26011709 | 2 |
| #26011693 | 2 |
| #26011691 | 2 |
| #26011687 | 2 |
| C4⋊C8×D173 | 2 |
| #26011486 | 2 |
| #462×C173 | 2 |
| #3035 | 173 |