Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26012206 | C2 | semidirect |
| 2. #26012162 | C2 | semidirect |
| 3. #26011838 | C2 | semidirect |
| 4. #26011816 | C2 | semidirect |
| 5. #26011787 | C2 | semidirect |
| 6. #26011727 | C2 | semidirect |
| 7. #26011687 | C2 | semidirect |
| 8. #26011638 | C2 | semidirect |
| 9. C4×#14583815 | C2 | semidirect |
| 10. #26011488 | C2 | semidirect |
| 11. C8×D4×C173 | C2 | semidirect |
| 132. C173 | #3305 | semidirect |
| 143. C8×D4 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012206 | 2 |
| #26012162 | 2 |
| #26011838 | 2 |
| #26011816 | 2 |
| #26011787 | 2 |
| #26011727 | 2 |
| #26011687 | 2 |
| #26011638 | 2 |
| C4×#14583815 | 2 |
| #26011488 | 2 |
| C8×D4×C173 | 2 |
| #3305 | 173 |