Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×C22⋊D67 |
| commutator | C4×C67 | C22×C8 |
| Frattini | C2×C8 | C22×D67 |
| Fitting | #504×C67 | C2 |
| socle | C2×C67 | C8×D4 |
| hypercenter | #504 | D67 |
| hypocenter | C67 | #2171 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C2×C16 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863812 | C2 | semidirect |
| 3. #16863216 | C2 | semidirect |
| 4. #16863181 | C2 | semidirect |
| 5. #16863180 | C2 | semidirect |
| 6. #16863171 | C2 | semidirect |
| 7. #504×C67 | C2 | semidirect |
| 72. C67 | #2171 | semidirect |
| 74. #504 | D67 | semidirect |