Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012162 | C2 | semidirect |
| 2. D4×Dic346 | C2 | semidirect |
| 3. #26011838 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011771 | C2 | semidirect |
| 6. #26011770 | C2 | semidirect |
| 7. #26011686 | C2 | semidirect |
| 8. #26011684 | C2 | semidirect |
| 9. C8×Dic346 | C2 | semidirect |
| 10. #26011571 | C2 | semidirect |
| 11. C4×D8×C173 | C2 | semidirect |
| 78. Dic346 | D8 | semidirect |
| 96. D4×C173 | #41 | semidirect |
| 131. C173 | #3358 | semidirect |
| 143. C4×D8 | D173 | semidirect |
| 222. D4 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012162 | 2 |
| D4×Dic346 | 2 |
| #26011838 | 2 |
| #26011836 | 2 |
| #26011771 | 2 |
| #26011770 | 2 |
| #26011686 | 2 |
| #26011684 | 2 |
| C8×Dic346 | 2 |
| #26011571 | 2 |
| C4×D8×C173 | 2 |
| #3358 | 173 |