Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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×C4⋊C4×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C4×C4⋊C4 | D67 |
| hypocenter | C67 | #2319 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16863292 | C2 | semidirect |
| 4. #16863287 | C2 | semidirect |
| 5. #16863258 | C2 | semidirect |
| 6. #16863255 | C2 | semidirect |
| 7. #16863242 | C2 | semidirect |
| 8. C4×C4⋊C4×C67 | C2 | semidirect |
| 11. C4×D268 | C4 | semidirect |
| 97. C67 | #2319 | semidirect |
| 104. C4×C4⋊C4 | D67 | semidirect |