Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
584 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#11745671 | C2 | semidirect |
| 3. C2×Q8×Dic59 | C2 | semidirect |
| 4. #16837600 | C2 | direct (N × H) |
| 5. C2×Dic59⋊C8 | C2 | semidirect |
| 6. C2×#14273649 | C2 | semidirect |
| 7. C2×#14273648 | C2 | semidirect |
| 8. C22×SD16×C59 | C2 | semidirect |
| 13. C2×#11745671 | C22 | semidirect |
| 18. Q8×Dic59 | C22 | semidirect |
| 23. Dic59⋊C8 | C22 | semidirect |
| 24. #14273649 | C22 | semidirect |
| 25. #14273648 | C22 | semidirect |
| 29. C2×SD16×C59 | C22 | semidirect |
| 35. C2×Q8×C59 | D4 | semidirect |
| 77. Q8×C59 | C2×D4 | semidirect |
| 92. C2×Dic59 | SD16 | semidirect |
| 118. Dic59 | C2×SD16 | semidirect |
| 121. C2×C59 | #460 | semidirect |
| 127. C22×SD16 | D59 | semidirect |
| 134. C59 | C2×#460 | semidirect |
| 143. C2×SD16 | C2×D59 | semidirect |
| 161. C2×Q8 | C22⋊D59 | semidirect |
| 203. Q8 | C2×C22⋊D59 | semidirect |
| 247. C2 | #16837600 | direct (N × H) |