Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic346 | C2 | semidirect |
| 3. #26011842 | C2 | semidirect |
| 4. #26011822 | C2 | semidirect |
| 5. #26011777 | C2 | semidirect |
| 6. #26011720 | C2 | semidirect |
| 7. #26011697 | C2 | semidirect |
| 8. #26011632 | C2 | semidirect |
| 9. C4×#14583815 | C2 | semidirect |
| 10. C2×#19149604 | C2 | semidirect |
| 11. C8×D4×C173 | C2 | semidirect |
| 83. Dic346 | #41 | semidirect |
| 96. D4×C173 | SD16 | semidirect |
| 128. C173 | #3298 | semidirect |
| 139. C8×D4 | D173 | semidirect |
| 217. D4 | #14583815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic346 | 2 |
| #26012145 | 2 |
| #26011842 | 2 |
| #26011822 | 2 |
| #26011777 | 2 |
| #26011720 | 2 |
| #26011697 | 2 |
| #26011632 | 2 |
| C4×#14583815 | 2 |
| C2×#19149604 | 2 |
| C8×D4×C173 | 2 |
| #3298 | 173 |