Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
240 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 77 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×#10596842 |
| commutator, socle | C22×C73 | C22×C8 |
| Fitting | C4⋊C4×C73 | C8 |
| hypercenter | C4⋊C4 | #10596842 |
| hypocenter | C73 | #1916 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 47. C4⋊Dic73 | C8 | semidirect |
| 48. #11924007 | C8 | semidirect |
| 49. #11924007 | C8 | semidirect |
| 50. C4⋊C4×C73 | C8 | semidirect |
| 111. C73 | #1916 | semidirect |
| 155. C4⋊C4 | #10596842 | semidirect |