Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 7. #19149734 | C4 | semidirect |
| 11. C4×#13063436 | C4 | semidirect |
| 12. C8×Dic173 | C4 | semidirect |
| 13. C4×C8×C173 | C4 | semidirect |
| 49. C173 | #1746 | semidirect |
| 62. C4×C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012450 | 2 |
| #26012427 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| C4×C8×D173 | 2 |
| #1746 | 173 |