Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14524015 |
| commutator | C2×C4×C67 | C22×C4 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #421×C67 | C2 |
| socle | C2×C67 | #386 |
| hypercenter | #421 | D67 |
| hypocenter | C67 | #1906 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #41×Dic67 | C2 | semidirect |
| 3. C2×#14523969 | C2 | semidirect |
| 4. #16863369 | C2 | semidirect |
| 5. #16863167 | C2 | semidirect |
| 6. #16863155 | C2 | semidirect |
| 7. #421×C67 | C2 | semidirect |
| 10. #14524073 | C4 | semidirect |
| 12. #14524068 | C4 | semidirect |
| 33. C2×Dic134 | C2×C4 | semidirect |
| 34. C2×D268 | C2×C4 | semidirect |
| 44. #11761612 | C2×C4 | semidirect |
| 130. C67 | #1906 | semidirect |
| 133. #421 | D67 | semidirect |