Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
564 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#64408 |
| commutator, socle | C23×C73 | C22×C4 |
| Fitting | C2×C4⋊C4×C73 | C4 |
| hypercenter | C2×C4⋊C4 | #64408 |
| hypocenter | C73 | #1441 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C2×C4⋊Dic73 | C4 | semidirect |
| 17. C2×#11924007 | C4 | semidirect |
| 18. C2×#11924007 | C4 | semidirect |
| 21. C2×C4⋊C4×C73 | C4 | semidirect |
| 93. C2×C4×C73 | C4⋊C4 | semidirect |
| 100. C2×Dic73 | C4⋊C4 | semidirect |
| 154. C73 | #1441 | semidirect |
| 172. C2×C4⋊C4 | #64408 | semidirect |
| 264. C2×C4 | C4⋊#64408 | semidirect |