Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
260 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #1939 |
| 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 |
|---|---|---|
| 36. C4⋊Dic73 | C8 | semidirect |
| 37. #11924007 | C8 | semidirect |
| 38. C4⋊C4×C73 | C8 | semidirect |
| 77. C4×C73 | C4⋊C8 | semidirect |
| 79. Dic73 | C4⋊C8 | semidirect |
| 88. C73 | #1939 | semidirect |
| 122. C4⋊C4 | #10596842 | semidirect |
| 167. C4 | C4⋊#10596842 | semidirect |