Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26011927 | C2 | semidirect |
| 2. #26011609 | C2 | semidirect |
| 3. #26011312 | C2 | semidirect |
| 4. #26011304 | C2 | semidirect |
| 5. #493×C173 | C2 | semidirect |
| 18. Dic692 | D4 | semidirect |
| 20. D1384 | D4 | semidirect |
| 61. C173 | #2213 | semidirect |
| 64. #493 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011927 | 2 |
| #26011609 | 2 |
| #26011312 | 2 |
| #26011304 | 2 |
| #493×C173 | 2 |
| #2213 | 173 |