Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #423×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #423 | D67 |
| hypocenter | C67 | #3038 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524071 | C2 | semidirect |
| 2. C2×#14524040 | C2 | semidirect |
| 3. C4×#11761628 | C2 | semidirect |
| 4. #16863597 | C2 | semidirect |
| 5. #16863592 | C2 | semidirect |
| 6. #16863402 | C2 | semidirect |
| 7. #423×C67 | C2 | semidirect |
| 12. C2×#11761617 | C22 | semidirect |
| 13. C2×D536 | C22 | semidirect |
| 17. C4×Dic134 | C22 | semidirect |
| 18. C4×D268 | C22 | semidirect |
| 23. #14523965 | C22 | semidirect |
| 26. C4⋊C8×C67 | C22 | semidirect |
| 29. #11761628 | D4 | semidirect |
| 78. D268 | C2×D4 | semidirect |
| 82. Dic134 | C2×D4 | semidirect |
| 94. C4×C67 | AGL(1,ℤ/8) | semidirect |
| 105. C67 | #3038 | semidirect |
| 111. #423 | D67 | semidirect |
| 130. C4⋊C8 | C2×D67 | semidirect |
| 201. C4 | #14524071 | semidirect |