Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
656 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 206 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. C2×C4⋊#10621924 | C4 | semidirect |
| 11. C2×C4×Dic173 | C4 | semidirect |
| 12. C2×C4×Dic173 | C4 | semidirect |
| 14. C2×C42×C173 | C4 | semidirect |
| 54. C2×Dic173 | C4⋊C4 | semidirect |
| 65. C2×C4×C173 | C4⋊C4 | semidirect |
| 84. C4×C173 | #95 | semidirect |
| 86. Dic173 | #95 | semidirect |
| 95. C173 | C4⋊#95 | semidirect |
| 109. C2×C42 | #10621924 | semidirect |
| 161. C2×C4 | C4⋊#10621924 | semidirect |
| 182. C4 | (C2×#10621924)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10621924 | 2 |
| C2×(C2×#10621924)⋊C4 | 2 |
| C2×C42×D173 | 2 |
| C4⋊#95 | 173 |