Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4 | C22×D53 |
| commutator | C2×C53 | C2×C4×C8 |
| Fitting | C53×#336 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | #336 | D53 |
| hypocenter | C53 | C8×C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #13133146 | C4 | semidirect |
| 16. C8×Dic53 | C4 | semidirect |
| 34. #11719919 | C8 | semidirect |
| 65. #88322 | C4⋊C4 | semidirect |
| 78. Dic53 | C4×C8 | semidirect |
| 92. C53 | C8×C4⋊C4 | semidirect |