Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. #26012211 | C2 | semidirect |
| 3. #26011842 | C2 | semidirect |
| 4. #26011833 | C2 | semidirect |
| 5. #26011772 | C2 | semidirect |
| 6. #26011732 | C2 | semidirect |
| 7. #26011702 | C2 | semidirect |
| 8. #26011655 | C2 | semidirect |
| 9. C4×#14583815 | C2 | semidirect |
| 10. #26011488 | C2 | semidirect |
| 11. C8×D4×C173 | C2 | semidirect |
| 125. C173 | #3302 | semidirect |
| 136. C8×D4 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012211 | 2 |
| #26012146 | 2 |
| #26011842 | 2 |
| #26011833 | 2 |
| #26011772 | 2 |
| #26011732 | 2 |
| #26011702 | 2 |
| #26011655 | 2 |
| C4×#14583815 | 2 |
| #26011488 | 2 |
| C8×D4×C173 | 2 |
| #3302 | 173 |