Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #391×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #391 | D67 |
| hypocenter | C67 | #2326 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic67 | C2 | semidirect |
| 5. #16863285 | C2 | semidirect |
| 6. #16863270 | C2 | semidirect |
| 7. #16863265 | C2 | semidirect |
| 8. #16863242 | C2 | semidirect |
| 9. #391×C67 | C2 | semidirect |
| 12. #14524032 | C4 | semidirect |
| 45. (C2×D67)⋊C4 | C2×C4 | semidirect |
| 47. C4×Dic67 | C2×C4 | semidirect |
| 51. C2×Q8×C67 | C2×C4 | semidirect |
| 112. C67 | #2326 | semidirect |
| 116. #391 | D67 | semidirect |
| 145. C2×Q8 | C4×D67 | semidirect |