Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 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. #26011284 | C2 | semidirect |
| 3. #353×C173 | C2 | semidirect |
| 6. #19149676 | C4 | semidirect |
| 8. C4×#13063436 | C4 | semidirect |
| 52. C173 | #1408 | semidirect |
| 56. #353 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011867 | 2 |
| #26011284 | 2 |
| #353×C173 | 2 |
| #1408 | 173 |