Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #400×C67 | C2 |
| hypercenter | #400 | D67 |
| hypocenter | C67 | #2828 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863325 | C2 | semidirect |
| 2. #16863314 | C2 | semidirect |
| 3. #16863313 | C2 | semidirect |
| 4. #16863313 | C2 | semidirect |
| 5. #16863306 | C2 | semidirect |
| 6. #16863306 | C2 | semidirect |
| 7. #16863297 | C2 | semidirect |
| 8. #16863285 | C2 | semidirect |
| 9. #400×C67 | C2 | semidirect |
| 135. C67 | #2828 | semidirect |
| 136. #400 | D67 | semidirect |