Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
408 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D53 |
| commutator, socle | C23×C53 | C22×C4 |
| Fitting | C2×C4×D4×C53 | C2 |
| hypercenter | C2×C4×D4 | D53 |
| hypocenter | C53 | #1870 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11719917 | C2 | semidirect |
| 2. C2×C22⋊#88322 | C2 | semidirect |
| 3. C2×C22⋊#88322 | C2 | semidirect |
| 4. #16810378 | C2 | semidirect |
| 50. C2×#88322 | D4 | semidirect |
| 60. C23×C53 | M16 | semidirect |
| 77. C2×C4×C53 | M16 | semidirect |
| 119. C53 | #1870 | semidirect |
| 173. C23 | #11719917 | semidirect |
| 190. C2×C4 | #11719917 | semidirect |