Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C22×C67 | C23×C4 |
| Fitting | #383×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #383 | D67 |
| hypocenter | C67 | C4×#126 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16863278 | C2 | semidirect |
| 4. #16863247 | C2 | semidirect |
| 6. C42×Dic67 | C2 | semidirect |
| 7. #383×C67 | C2 | semidirect |
| 9. #14524037 | C4 | semidirect |
| 28. Dic67⋊C4 | C2×C4 | semidirect |
| 37. C42×C67 | C2×C4 | semidirect |
| 68. Dic67 | #126 | semidirect |
| 74. C67 | C4×#126 | semidirect |
| 78. #383 | D67 | semidirect |
| 111. C42 | C4×D67 | semidirect |