Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C22×C53 | C2×C42 |
| Fitting | C4×C22⋊C4×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C4×C22⋊C4 | D53 |
| hypocenter | C53 | #1753 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#13133128 | C2 | semidirect |
| 4. C2×C4×#88322 | C2 | semidirect |
| 5. #16810378 | C2 | semidirect |
| 6. #16810378 | C2 | semidirect |
| 10. C2×#11719917 | C4 | semidirect |
| 15. C22⋊#88322 | C4 | semidirect |
| 70. C2×C4×C53 | M16 | semidirect |
| 80. #88322 | C22⋊C4 | semidirect |
| 112. C53 | #1753 | semidirect |
| 174. C2×C4 | #11719917 | semidirect |