Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C22×C42×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C22×C42 | D67 |
| hypocenter | C67 | C22×#124 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic134 | C2 | semidirect |
| 3. C2×#14524031 | C2 | direct (N × H) |
| 4. C22×(C2×D67)⋊C4 | C2 | semidirect |
| 5. C22×C42×C67 | C2 | semidirect |
| 8. C22×Dic134 | C22 | semidirect |
| 12. #14524031 | C22 | direct (N × H) |
| 13. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 16. C2×C42×C67 | C22 | semidirect |
| 21. C2×Dic134 | C23 | semidirect |
| 26. (C2×D67)⋊C4 | C23 | semidirect |
| 32. C42×C67 | C23 | semidirect |
| 48. C22×C67 | #124 | semidirect |
| 58. C2×C67 | C2×#124 | semidirect |
| 63. C67 | C22×#124 | semidirect |
| 68. C22×C42 | D67 | semidirect |
| 79. C2×C42 | C2×D67 | semidirect |
| 95. C42 | C22×D67 | semidirect |
| 114. C22 | #14524031 | direct (N × H) |
| 122. C2 | C2×#14524031 | direct (N × H) |