Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14524011 |
| commutator | C42×C67 | C23 |
| Frattini | C42 | C22×D67 |
| Fitting | #477×C67 | C2 |
| socle | C22×C67 | #120 |
| hypercenter | #477 | D67 |
| hypocenter | C67 | #1631 |
| LCS | G ▷ C42×C67 ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #477 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863770 | C2 | semidirect |
| 3. #16863683 | C2 | semidirect |
| 4. #16863139 | C2 | semidirect |
| 5. Q8⋊(C67⋊C8) | C2 | semidirect |
| 6. #16863123 | C2 | semidirect |
| 7. #477×C67 | C2 | semidirect |
| 54. Q8×C67 | SD16 | semidirect |
| 99. C67 | #1631 | semidirect |
| 102. #477 | D67 | semidirect |
| 153. Q8 | #11761615 | semidirect |