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 |
| 2. #26011843 | C2 | semidirect |
| 3. #26011821 | C2 | semidirect |
| 4. #26011773 | C2 | semidirect |
| 5. #26011718 | C2 | semidirect |
| 6. #26011696 | C2 | semidirect |
| 7. #26011629 | C2 | semidirect |
| 8. C4×#14583814 | C2 | semidirect |
| 9. D4×#13063436 | C2 | semidirect |
| 10. C2×#19149602 | C2 | semidirect |
| 81. Dic346 | #41 | semidirect |
| 95. D4×C173 | SD16 | semidirect |
| 128. C173 | #3298 | semidirect |
| 217. D4 | #14583814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic346 | 2 |
| #26011843 | 2 |
| #26011821 | 2 |
| #26011773 | 2 |
| #26011718 | 2 |
| #26011696 | 2 |
| #26011629 | 2 |
| C4×#14583814 | 2 |
| D4×#13063436 | 2 |
| C2×#19149602 | 2 |
| #547×C173 | 2 |
| #3298 | 173 |