Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012023 | C2 | semidirect |
| 2. #26011892 | C2 | semidirect |
| 3. #26011874 | C2 | semidirect |
| 4. #26011844 | C2 | semidirect |
| 5. #26011733 | C2 | semidirect |
| 7. #26011719 | C2 | semidirect |
| 8. C4×Dic692 | C2 | semidirect |
| 9. C4×#14583814 | C2 | semidirect |
| 10. C4×C8×D173 | C2 | semidirect |
| 11. C4×D8×C173 | C2 | semidirect |
| 118. C173 | #3168 | semidirect |
| 129. C4×D8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012023 | 2 |
| #26011892 | 2 |
| #26011874 | 2 |
| #26011844 | 2 |
| #26011733 | 2 |
| #26011724 | 2 |
| #26011719 | 2 |
| C4×Dic692 | 2 |
| C4×#14583814 | 2 |
| C4×C8×D173 | 2 |
| C4×D8×C173 | 2 |
| #3168 | 173 |