Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26011515 | C2 | semidirect |
| 4. #26011259 | C2 | semidirect |
| 5. #423×C173 | C2 | semidirect |
| 91. C4×C173 | #100 | semidirect |
| 103. C173 | #1800 | semidirect |
| 107. #423 | D173 | semidirect |
| 196. C4 | #19149595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| #26011515 | 2 |
| C2×#19149595 | 2 |
| #26011259 | 2 |
| #423×C173 | 2 |
| #1800 | 173 |