Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
292 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 292 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 | C22⋊C4×C73 | C8 |
| hypercenter | C22⋊C4 | #10596842 |
| hypocenter | C73 | #1923 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊#10596842 | C2 | semidirect |
| 4. C2×C4×#10596842 | C2 | semidirect |
| 5. (C2×#10596842)⋊C4 | C2 | semidirect |
| 6. (C2×#10596842)⋊C4 | C2 | semidirect |
| 53. C22⋊Dic73 | C8 | semidirect |
| 54. #11924005 | C8 | semidirect |
| 55. #11924005 | C8 | semidirect |
| 56. C22⋊C4×C73 | C8 | semidirect |
| 135. C73 | #1923 | semidirect |
| 187. C22⋊C4 | #10596842 | semidirect |