Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 177 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. #26011549 | C2 | semidirect |
| 3. #26011541 | C2 | semidirect |
| 4. #26011519 | C2 | semidirect |
| 5. #26011517 | C2 | semidirect |
| 7. M16×Dic173 | C2 | semidirect |
| 8. C2×C8×Dic173 | C2 | semidirect |
| 93. C173 | #2922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic173 | 2 |
| #26011549 | 2 |
| #26011541 | 2 |
| #26011519 | 2 |
| #26011517 | 2 |
| #26011458 | 2 |
| M16×Dic173 | 2 |
| C2×C8×Dic173 | 2 |
| #408×C173 | 2 |
| #2922 | 173 |