Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
300 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#14583805 | C4 | semidirect |
| 10. C2×C4×Dic173 | C4 | semidirect |
| 11. C2×C42×C173 | C4 | semidirect |
| 55. C173 | #1820 | semidirect |
| 66. C2×C42 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012434 | 2 |
| #26012369 | 2 |
| C2×#19149636 | 2 |
| #1820 | 173 |