Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19149604 | C2 | semidirect |
| 4. #26011254 | C2 | semidirect |
| 8. #19149658 | C4 | semidirect |
| 75. C22×C173 | #103 | semidirect |
| 94. C173 | #1892 | semidirect |
| 170. C22 | #19149604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| C2×#19149604 | 2 |
| #26011351 | 2 |
| #26011254 | 2 |
| C23×C8×C173 | 2 |
| #1892 | 173 |