Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. Q32×D173 | C2 | semidirect |
| 3. Dic2768 | C2 | semidirect |
| 4. #26011331 | C2 | semidirect |
| 5. #26011329 | C2 | semidirect |
| 6. #26011324 | C2 | semidirect |
| 7. SD64×C173 | C2 | semidirect |
| 51. C173 | #2264 | semidirect |
| 58. SD64 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011920 | 2 |
| Q32×D173 | 2 |
| Dic2768 | 2 |
| #26011331 | 2 |
| #26011329 | 2 |
| #26011324 | 2 |
| SD64×C173 | 2 |
| #2264 | 173 |