Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 266 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 | C4 | #14524029 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #413×C67 | C2 |
| socle | C2×C67 | #394 |
| hypercenter | #413 | D67 |
| hypocenter | C67 | #2050 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #413 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863419 | C2 | semidirect |
| 3. C2×#14523970 | C2 | semidirect |
| 4. C2×#14523969 | C2 | semidirect |
| 5. #16863378 | C2 | semidirect |
| 6. C67⋊#338 | C2 | semidirect |
| 7. #413×C67 | C2 | semidirect |
| 123. C67 | #2050 | semidirect |
| 129. #413 | D67 | semidirect |