Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
608 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 150 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×#6157 |
| commutator, socle | C23×C53 | C22×C4 |
| Fitting | #95×C53 | C4 |
| hypercenter | #95 | #6157 |
| hypocenter | C53 | #1444 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #13133124 | C4 | semidirect |
| 11. #95×C53 | C4 | semidirect |
| 44. C2×C4×C53 | C4⋊C4 | semidirect |
| 46. C2×Dic53 | C4⋊C4 | semidirect |
| 77. C53 | #1444 | semidirect |
| 85. #95 | #6157 | semidirect |
| 123. C2×C4 | C4⋊#6157 | semidirect |