Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
872 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 237 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×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | C4×C22⋊C4×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C4×C22⋊C4 | D67 |
| hypocenter | C67 | #2341 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×Dic134 | C2 | semidirect |
| 3. #16863298 | C2 | semidirect |
| 4. #16863296 | C2 | semidirect |
| 5. #16863256 | C2 | semidirect |
| 6. #16863255 | C2 | semidirect |
| 7. #16863243 | C2 | semidirect |
| 8. C4×C22⋊C4×C67 | C2 | semidirect |
| 10. C2×#11761628 | C4 | semidirect |
| 76. C2×C4×C67 | #41 | semidirect |
| 85. Dic134 | C22⋊C4 | semidirect |
| 115. C67 | #2341 | semidirect |
| 123. C4×C22⋊C4 | D67 | semidirect |
| 200. C2×C4 | #11761628 | semidirect |