Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
146 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×#6157 |
| commutator | C4×C53 | C22×C8 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | #104×C53 | C4 |
| socle | C2×C53 | C8×D4 |
| hypercenter | #104 | #6157 |
| hypocenter | C53 | #2170 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #104 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811682 | C2 | semidirect |
| 2. #16811681 | C2 | semidirect |
| 3. #16811546 | C2 | semidirect |
| 4. #16811522 | C2 | semidirect |
| 5. #16811521 | C2 | semidirect |
| 6. C4×#11719910 | C2 | semidirect |
| 79. C53 | #2170 | semidirect |