Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
190 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14524029 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #344×C67 | C2 |
| socle | C2×C67 | #397 |
| hypercenter | #344 | D67 |
| hypocenter | C67 | #2080 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #344 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863424 | C2 | semidirect |
| 5. #16863160 | C2 | semidirect |
| 6. #16863152 | C2 | semidirect |
| 7. #344×C67 | C2 | semidirect |
| 90. C67 | #2080 | semidirect |
| 95. #344 | D67 | semidirect |