Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C4⋊#6157 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | #97×C53 | C4 |
| socle | C22×C53 | C2×C4⋊C4 |
| hypercenter | #97 | #6157 |
| hypocenter | C53 | #1776 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #13133286 | C4 | semidirect |
| 10. #13133285 | C4 | semidirect |
| 15. #13133128 | C4 | semidirect |
| 16. #13133127 | C4 | semidirect |
| 17. #13133127 | C4 | semidirect |
| 18. #97×C53 | C4 | semidirect |
| 57. C8×C53 | C42 | semidirect |
| 59. #88322 | C42 | semidirect |
| 84. C53 | #1776 | semidirect |
| 96. #97 | #6157 | semidirect |
| 138. C8 | C4×#6157 | semidirect |