Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
296 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 124 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 | C2×C53 | C2×C4×C8 |
| Fitting | C4⋊C8×C53 | C4 |
| socle | C22×C53 | C2×C42 |
| hypercenter | C4⋊C8 | #6157 |
| hypocenter | C53 | C8×C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×#88324 | C4 | semidirect |
| 11. C4×#88324 | C4 | semidirect |
| 16. C4⋊#88322 | C4 | semidirect |
| 17. #13133146 | C4 | semidirect |
| 18. C4⋊C8×C53 | C4 | semidirect |
| 25. C4⋊#6157 | C8 | semidirect |
| 57. #88324 | C4⋊C4 | semidirect |
| 67. C4×C53 | C4×C8 | semidirect |
| 71. Dic53 | C4×C8 | semidirect |
| 85. C53 | C8×C4⋊C4 | semidirect |
| 94. C4⋊C8 | #6157 | semidirect |
| 151. C4 | C8×#6157 | semidirect |