Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #390×C67 | C2 |
| hypercenter | #390 | D67 |
| hypocenter | C67 | #2432 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524043 | C2 | semidirect |
| 3. C2×#14524030 | C2 | semidirect |
| 4. C2×#14524023 | C2 | semidirect |
| 5. #16863312 | C2 | semidirect |
| 6. #16863301 | C2 | semidirect |
| 7. #16863271 | C2 | semidirect |
| 8. C4×(C2×D67)⋊C4 | C2 | semidirect |
| 9. #390×C67 | C2 | semidirect |
| 89. C2×C4×C67 | #41 | semidirect |
| 137. C67 | #2432 | semidirect |
| 144. #390 | D67 | semidirect |
| 243. C2×C4 | #11761627 | semidirect |