Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012215 | C2 | semidirect |
| 2. #26012202 | C2 | semidirect |
| 3. #26011847 | C2 | semidirect |
| 4. #26011800 | C2 | semidirect |
| 5. #26011778 | C2 | semidirect |
| 7. #26011693 | C2 | semidirect |
| 8. C8×Dic346 | C2 | semidirect |
| 9. #26011576 | C2 | semidirect |
| 11. #487×C173 | C2 | semidirect |
| 120. C173 | #3360 | semidirect |
| 125. #487 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012215 | 2 |
| #26012202 | 2 |
| #26011847 | 2 |
| #26011800 | 2 |
| #26011778 | 2 |
| #26011709 | 2 |
| #26011693 | 2 |
| C8×Dic346 | 2 |
| #26011576 | 2 |
| C4×D1384 | 2 |
| #487×C173 | 2 |
| #3360 | 173 |