Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
788 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C53×#384 | C2 |
| hypercenter | #384 | D53 |
| hypocenter | C53 | #2537 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133192 | C2 | semidirect |
| 2. C2×C4×D212 | C2 | semidirect |
| 3. #16810540 | C2 | semidirect |
| 4. #16810480 | C2 | semidirect |
| 5. C53×#384 | C2 | semidirect |
| 27. C2×D212 | D4 | semidirect |
| 33. C42×C53 | D4 | semidirect |
| 73. C4×C53 | #121 | semidirect |
| 85. #384 | D53 | semidirect |
| 87. C53 | #2537 | semidirect |
| 118. C42 | D212 | semidirect |
| 156. C4 | #13133192 | semidirect |