Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator, socle | C22×C113 | C22×C4 |
| Fitting | C4⋊C4×C113 | C4 |
| hypercenter | C4⋊C4 | #90673 |
| hypocenter | C113 | #389 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C4⋊Dic113 | C4 | semidirect |
| 15. #14268626 | C4 | semidirect |
| 16. C4⋊C4×C113 | C4 | semidirect |
| 46. C4×C113 | C4⋊C4 | semidirect |
| 48. Dic113 | C4⋊C4 | semidirect |
| 56. C113 | #389 | semidirect |
| 72. C4⋊C4 | #90673 | semidirect |
| 105. C4 | C4⋊#90673 | semidirect |