Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D67 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #340×C67 | C2 |
| socle | C23×C67 | C2×D4 |
| hypercenter | #340 | D67 |
| hypocenter | C67 | #2034 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14523974 | C2 | semidirect |
| 3. C2×#14523965 | C2 | semidirect |
| 4. C2×#14523963 | C2 | semidirect |
| 5. C2×(C2×D67)⋊C8 | C2 | semidirect |
| 6. #16863253 | C2 | semidirect |
| 7. #340×C67 | C2 | semidirect |
| 46. C2×C67⋊C8 | D4 | semidirect |
| 144. C67 | #2034 | semidirect |
| 151. #340 | D67 | semidirect |