Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 8. #19149750 | C4 | semidirect |
| 9. #19149749 | C4 | semidirect |
| 68. C173 | #1778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149750 | 2 |
| C2×#19149749 | 2 |
| C4×#14583836 | 2 |
| #26012367 | 2 |
| #97×D173 | 2 |
| #1778 | 173 |