Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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 | C2×C4×C67 | C22×C4 |
| Frattini | C42 | C22×D67 |
| Fitting | #335×C67 | C2 |
| socle | C22×C67 | C4×D4 |
| hypercenter | #335 | D67 |
| hypocenter | C67 | #1592 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 1. #16863523 | C2 | semidirect |
| 4. #16863126 | C2 | semidirect |
| 6. #16863117 | C2 | semidirect |
| 7. #335×C67 | C2 | semidirect |
| 57. C8×C67 | M16 | semidirect |
| 78. C67 | #1592 | semidirect |
| 82. #335 | D67 | semidirect |
| 138. C8 | #11761611 | semidirect |