Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #424×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #424 | D67 |
| hypocenter | C67 | #3083 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864024 | C2 | semidirect |
| 3. #16863704 | C2 | semidirect |
| 4. #16863697 | C2 | semidirect |
| 5. #16863692 | C2 | semidirect |
| 6. #16863677 | C2 | semidirect |
| 7. #16863438 | C2 | semidirect |
| 8. C2×#14523977 | C2 | semidirect |
| 11. #424×C67 | C2 | semidirect |
| 42. #11761628 | Q8 | semidirect |
| 124. C67 | #3083 | semidirect |
| 133. #424 | D67 | semidirect |