Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic346 | C2 | semidirect |
| 3. #26011837 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011782 | C2 | semidirect |
| 6. #26011779 | C2 | semidirect |
| 7. #26011689 | C2 | semidirect |
| 8. #26011615 | C2 | semidirect |
| 9. SD16×Dic173 | C2 | semidirect |
| 10. C4×#14583813 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 77. Dic346 | SD16 | semidirect |
| 92. Q8×C173 | #41 | semidirect |
| 125. C173 | #3362 | semidirect |
| 134. #460 | D173 | semidirect |
| 206. Q8 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic346 | 2 |
| #26012161 | 2 |
| #26011837 | 2 |
| #26011836 | 2 |
| #26011782 | 2 |
| #26011779 | 2 |
| #26011689 | 2 |
| #26011615 | 2 |
| SD16×Dic173 | 2 |
| C4×#14583813 | 2 |
| #460×C173 | 2 |
| #3362 | 173 |