Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C2×#14524074 | C2 | semidirect |
| 2. C2×M16×D67 | C2 | semidirect |
| 4. C2×#14524019 | C2 | semidirect |
| 5. #16863653 | C2 | semidirect |
| 6. #16863645 | C2 | semidirect |
| 7. #16863636 | C2 | semidirect |
| 8. #16863628 | C2 | semidirect |
| 9. #16863439 | C2 | semidirect |
| 10. #16863398 | C2 | semidirect |
| 11. #419×C67 | C2 | semidirect |
| 15. C2×#11761618 | C22 | semidirect |
| 16. C2×#11761615 | C22 | semidirect |
| 36. #14523976 | C22 | semidirect |
| 37. #14523974 | C22 | semidirect |
| 38. #14523968 | C22 | semidirect |
| 39. #14523965 | C22 | semidirect |
| 43. #103×C67 | C22 | semidirect |
| 44. #103×C67 | C22 | semidirect |
| 64. #11761612 | D4 | semidirect |
| 145. C2×D67 | #137 | semidirect |
| 164. C67 | #3056 | semidirect |
| 174. #419 | D67 | semidirect |
| 206. #103 | C2×D67 | semidirect |
| 207. #103 | C2×D67 | semidirect |