Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D67 |
| commutator | C4×C67 | C22×C8 |
| Frattini | C42 | C22×D67 |
| Fitting | #335×C67 | C2 |
| socle | C22×C67 | C2×C4⋊C4 |
| hypercenter | #335 | D67 |
| hypocenter | C67 | #1565 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #335 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #16863148 | C2 | semidirect |
| 5. #16863147 | C2 | semidirect |
| 6. #16863146 | C2 | semidirect |
| 7. #335×C67 | C2 | semidirect |
| 27. #11761611 | C8 | semidirect |
| 56. C8×C67 | C2×C8 | semidirect |
| 60. C67⋊C8 | C2×C8 | semidirect |
| 78. C67 | #1565 | semidirect |
| 83. #335 | D67 | semidirect |
| 138. C8 | C8×D67 | semidirect |