Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
172 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 44 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×#6157)⋊C4 |
| commutator | C2×C4×C53 | C42 |
| Frattini | C42 | C2×#6157 |
| Fitting | #97×C53 | C4 |
| socle | C22×C53 | #95 |
| hypercenter | #97 | #6157 |
| hypocenter | C53 | #1300 |
| LCS | G ▷ C2×C4×C53 ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C4⋊#88324 | C4 | semidirect |
| 12. #13133128 | C4 | semidirect |
| 14. #97×C53 | C4 | semidirect |
| 63. C53 | #1300 | semidirect |
| 71. #97 | #6157 | semidirect |