Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6157 |
| commutator, socle | C22×C53 | C2×C42 |
| Fitting | C4×C8×C53 | C4 |
| hypercenter | C4×C8 | #6157 |
| hypocenter | C53 | #1770 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #13133284 | C4 | semidirect |
| 10. C4⋊#88324 | C4 | semidirect |
| 16. C4×#88322 | C4 | semidirect |
| 17. C8×Dic53 | C4 | semidirect |
| 18. C8×Dic53 | C4 | semidirect |
| 19. C4×C8×C53 | C4 | semidirect |
| 60. C8×C53 | C4⋊C4 | semidirect |
| 62. #88322 | C4⋊C4 | semidirect |
| 70. C4×C53 | #97 | semidirect |
| 74. Dic53 | #97 | semidirect |
| 88. C53 | #1770 | semidirect |
| 101. C4×C8 | #6157 | semidirect |
| 145. C8 | C4⋊#6157 | semidirect |
| 157. C4 | #13133271 | semidirect |