Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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. C22×Q8×D59 | C2 | semidirect |
| 3. C2×#14273756 | C2 | direct (N × H) |
| 4. C22×Dic236 | C2 | semidirect |
| 5. C22×#11745672 | C2 | semidirect |
| 6. C22×#11745670 | C2 | semidirect |
| 7. C22×#11745659 | C2 | semidirect |
| 8. C22×SD16×C59 | C2 | semidirect |
| 15. C2×Q8×D59 | C22 | semidirect |
| 20. #14273756 | C22 | direct (N × H) |
| 21. C2×Dic236 | C22 | semidirect |
| 22. C2×#11745672 | C22 | semidirect |
| 23. C2×#11745670 | C22 | semidirect |
| 24. C2×#11745659 | C22 | semidirect |
| 28. C2×SD16×C59 | C22 | semidirect |
| 44. Q8×D59 | C23 | semidirect |
| 55. SD16×C59 | C23 | semidirect |
| 57. #11745672 | C23 | semidirect |
| 58. #11745670 | C23 | semidirect |
| 60. Dic236 | C23 | semidirect |
| 61. #11745659 | C23 | semidirect |
| 91. C22×C59 | #137 | semidirect |
| 103. C2×C59 | C2×#137 | semidirect |
| 112. C22×SD16 | D59 | semidirect |
| 114. C59 | C22×#137 | semidirect |
| 132. C2×SD16 | C2×D59 | semidirect |
| 164. SD16 | C22×D59 | semidirect |
| 199. C22 | #14273756 | direct (N × H) |
| 209. C2 | C2×#14273756 | direct (N × H) |