Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524072 | C2 | semidirect |
| 3. C22⋊Q8×D67 | C2 | semidirect |
| 4. #16863559 | C2 | semidirect |
| 5. #16863555 | C2 | semidirect |
| 6. #16863554 | C2 | semidirect |
| 7. #16863551 | C2 | semidirect |
| 8. #16863547 | C2 | semidirect |
| 9. #16863394 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #450×C67 | C2 | semidirect |
| 18. C2×Q8×D67 | C22 | semidirect |
| 23. C2×Dic268 | C22 | semidirect |
| 24. C2×#11761618 | C22 | semidirect |
| 25. C2×#11761616 | C22 | semidirect |
| 26. C2×#11761611 | C22 | semidirect |
| 27. #14524023 | C22 | semidirect |
| 31. #14524019 | C22 | semidirect |
| 33. C4⋊C4×D67 | C22 | semidirect |
| 35. #14523968 | C22 | semidirect |
| 36. #14523966 | C22 | semidirect |
| 37. #14523964 | C22 | semidirect |
| 39. (C2×D67)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C67 | C22 | semidirect |
| 43. #102×C67 | C22 | semidirect |
| 146. C22×C67 | #137 | semidirect |
| 172. C67 | #3007 | semidirect |
| 181. #450 | D67 | semidirect |
| 199. C2×SD16 | C2×D67 | semidirect |
| 213. #102 | C2×D67 | semidirect |
| 325. C22 | #14524072 | semidirect |