Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14524040 |
| commutator | C42×C67 | C23 |
| Frattini | C42 | C22×D67 |
| Fitting | #322×C67 | C2 |
| socle | C22×C67 | #127 |
| hypercenter | #322 | D67 |
| hypocenter | C67 | #1714 |
| LCS | G ▷ C42×C67 ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #322 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863801 | C2 | semidirect |
| 2. #16863794 | C2 | semidirect |
| 5. #16863747 | C2 | semidirect |
| 7. #322×C67 | C2 | semidirect |
| 54. C8×C67 | SD16 | semidirect |
| 70. C67 | #1714 | semidirect |
| 77. #322 | D67 | semidirect |
| 124. C8 | #11761617 | semidirect |