Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D53 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#340 | C2 |
| socle | C23×C53 | C2×D4 |
| hypercenter | #340 | D53 |
| hypocenter | C53 | C4×#102 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C8×Dic53 | C2 | semidirect |
| 5. C4⋊C4×Dic53 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C53×#340 | C2 | semidirect |
| 12. #13133179 | C4 | semidirect |
| 17. #13133139 | C4 | semidirect |
| 18. #13133137 | C4 | semidirect |
| 42. C2×C8×C53 | C2×C4 | semidirect |
| 46. C4⋊C4×C53 | C2×C4 | semidirect |
| 49. C4⋊Dic53 | C2×C4 | semidirect |
| 55. C2×#88322 | C2×C4 | semidirect |
| 88. D212 | C42 | semidirect |
| 114. Dic53 | #102 | semidirect |
| 130. #340 | D53 | semidirect |
| 131. C53 | C4×#102 | semidirect |
| 169. C2×C8 | C4×D53 | semidirect |
| 175. C4⋊C4 | C4×D53 | semidirect |