Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26011515 | C2 | semidirect |
| 3. #26011260 | C2 | semidirect |
| 70. C4×C173 | #100 | semidirect |
| 79. C173 | #1800 | semidirect |
| 150. C4 | #19149596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011515 | 2 |
| C2×#19149596 | 2 |
| #26011260 | 2 |
| C2×C4×D4×C173 | 2 |
| #1800 | 173 |