Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator, socle | C23×C67 | C24 |
| Frattini | C23 | C23×D67 |
| Fitting | C4×C22⋊C4×C67 | C2 |
| hypercenter | C4×C22⋊C4 | D67 |
| hypocenter | C67 | #2395 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524002 | C2 | semidirect |
| 3. #16863336 | C2 | semidirect |
| 4. #16863333 | C2 | semidirect |
| 5. #16863328 | C2 | semidirect |
| 6. #16863323 | C2 | semidirect |
| 7. #16863321 | C2 | semidirect |
| 9. C4×C4⋊Dic67 | C2 | semidirect |
| 10. C4×(C2×D67)⋊C4 | C2 | semidirect |
| 11. C4×C22⋊C4×C67 | C2 | semidirect |
| 138. C67 | #2395 | semidirect |
| 149. C4×C22⋊C4 | D67 | semidirect |