Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
600 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 210 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 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C2×C4⋊C4×C53 | C4 |
| hypercenter | C2×C4⋊C4 | #6157 |
| hypocenter | C53 | #2316 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16811574 | C2 | semidirect |
| 13. C2×C4⋊Dic53 | C4 | semidirect |
| 14. C2×#11719919 | C4 | semidirect |
| 15. C4⋊C4×D53 | C4 | semidirect |
| 17. C2×C4⋊C4×C53 | C4 | semidirect |
| 49. C2×C4×C53 | C4⋊C4 | semidirect |
| 53. C2×Dic53 | C4⋊C4 | semidirect |
| 58. C4×D53 | C4⋊C4 | semidirect |
| 91. C53 | #2316 | semidirect |
| 101. C2×C4⋊C4 | #6157 | semidirect |
| 145. C2×C4 | C4⋊#6157 | semidirect |