Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D173 | C2 | semidirect |
| 3. #26011806 | C2 | semidirect |
| 4. #26011783 | C2 | semidirect |
| 5. #26011692 | C2 | semidirect |
| 6. #26011691 | C2 | semidirect |
| 7. #26011631 | C2 | semidirect |
| 8. #26011594 | C2 | semidirect |
| 9. #26011590 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #477×C173 | C2 | semidirect |
| 87. Dic346 | #41 | semidirect |
| 108. Q8×C173 | #41 | semidirect |
| 140. C173 | #3112 | semidirect |
| 146. #477 | D173 | semidirect |
| 231. Q8 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012042 | 2 |
| C4×Q8×D173 | 2 |
| #26011806 | 2 |
| #26011783 | 2 |
| #26011692 | 2 |
| #26011691 | 2 |
| #26011631 | 2 |
| #26011594 | 2 |
| #26011590 | 2 |
| #26011547 | 2 |
| #477×C173 | 2 |
| #3112 | 173 |