Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D67 |
| commutator | C22×C67 | C22×C8 |
| Fitting | #336×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | #336 | D67 |
| hypocenter | C67 | #1850 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊(C67⋊C8) | C2 | semidirect |
| 3. C2×Dic67⋊C8 | C2 | semidirect |
| 6. #16863150 | C2 | semidirect |
| 7. #336×C67 | C2 | semidirect |
| 43. (C2×D67)⋊C4 | C8 | semidirect |
| 70. C2×C4×C67 | C2×C8 | semidirect |
| 85. C2×Dic67 | C2×C8 | semidirect |
| 107. C2×D67 | C4⋊C8 | semidirect |
| 126. C67 | #1850 | semidirect |
| 133. #336 | D67 | semidirect |
| 209. C2×C4 | C8×D67 | semidirect |