Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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×D67 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #340×C67 | C2 |
| socle | C23×C67 | C2×D4 |
| hypercenter | #340 | D67 |
| hypocenter | C67 | #2025 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524034 | C2 | semidirect |
| 5. #16863158 | C2 | semidirect |
| 6. #16863150 | C2 | semidirect |
| 7. #340×C67 | C2 | semidirect |
| 121. C67 | #2025 | semidirect |
| 127. #340 | D67 | semidirect |