Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | #380×C67 | C2 |
| hypercenter | #380 | D67 |
| hypocenter | C67 | #2549 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863329 | C2 | semidirect |
| 3. #16863316 | C2 | semidirect |
| 4. #16863300 | C2 | semidirect |
| 5. #16863293 | C2 | semidirect |
| 48. C22⋊Dic67 | Q8 | semidirect |
| 52. C22×C4×C67 | Q8 | semidirect |
| 115. C67 | #2549 | semidirect |
| 159. C22×C4 | Dic134 | semidirect |