Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×Q8×Dic173 | C2 | semidirect |
| 3. #26011805 | C2 | semidirect |
| 4. #26011802 | C2 | semidirect |
| 5. #26011784 | C2 | semidirect |
| 6. #26011689 | C2 | semidirect |
| 7. #26011630 | C2 | semidirect |
| 8. #26011594 | C2 | semidirect |
| 9. #26011592 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #448×C173 | C2 | semidirect |
| 104. Q8×C173 | #41 | semidirect |
| 140. C173 | #3112 | semidirect |
| 149. #448 | D173 | semidirect |
| 229. Q8 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012036 | 2 |
| C2×Q8×Dic173 | 2 |
| #26011805 | 2 |
| #26011802 | 2 |
| #26011784 | 2 |
| #26011689 | 2 |
| #26011630 | 2 |
| #26011594 | 2 |
| #26011592 | 2 |
| #26011545 | 2 |
| #448×C173 | 2 |
| #3112 | 173 |