Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 5. #19149738 | C4 | semidirect |
| 8. C2×C4×Dic173 | C4 | semidirect |
| 9. C2×C4⋊C4×C173 | C4 | semidirect |
| 71. C173 | #1393 | semidirect |
| 76. C2×C4⋊C4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149738 | 2 |
| #26011392 | 2 |
| #1393 | 173 |