Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
272 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#10596842 |
| commutator | C2×C73 | C22×C16 |
| Frattini | C22 | C22×#10596842 |
| Fitting | C24×C73 | C8 |
| socle | C23×C73 | C2×C8 |
| hypercenter | C24 | #10596842 |
| hypocenter | C73 | C2×C22⋊C16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11924040 | C2 | semidirect |
| 2. C22⋊#11924040 | C2 | direct (N × H) |
| 5. C2×#11924040 | C22 | semidirect |
| 29. C23×C73 | C16 | semidirect |
| 49. C22×C73 | C2×C16 | semidirect |
| 57. C2×C73 | C22⋊C16 | semidirect |
| 62. C73 | C2×C22⋊C16 | semidirect |
| 91. C23 | #11924040 | semidirect |
| 111. C22 | C2×#11924040 | semidirect |
| 119. C2 | C22⋊#11924040 | direct (N × H) |