Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
324 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6157 |
| commutator, socle | C23×C53 | C22×C4 |
| Fitting | C2×C22⋊C4×C53 | C4 |
| hypercenter | C2×C22⋊C4 | #6157 |
| hypocenter | C53 | #1851 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133284 | C2 | semidirect |
| 3. C2×C4⋊#88324 | C2 | semidirect |
| 5. #16811489 | C2 | semidirect |
| 6. #16811489 | C2 | semidirect |
| 70. C2×C4×C53 | M16 | semidirect |
| 83. C2×Dic53 | M16 | semidirect |
| 133. C53 | #1851 | semidirect |
| 215. C2×C4 | #11719940 | semidirect |