Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26011539 | C2 | semidirect |
| 2. #26011519 | C2 | semidirect |
| 3. #26011518 | C2 | semidirect |
| 6. #26011247 | C2 | semidirect |
| 89. C173 | #2098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011539 | 2 |
| #26011519 | 2 |
| #26011518 | 2 |
| #26011508 | 2 |
| #26011458 | 2 |
| #26011247 | 2 |
| #421×C173 | 2 |
| #2098 | 173 |