Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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×#11745685 | C2 | semidirect |
| 2. C2×#14273753 | C2 | direct (N × H) |
| 3. C22×#11745670 | C2 | semidirect |
| 4. C22×#11745669 | C2 | semidirect |
| 5. C22×#11745664 | C2 | semidirect |
| 6. C23×D4×C59 | C2 | semidirect |
| 8. C2×#11745685 | C22 | semidirect |
| 9. C22×Dic118 | C22 | semidirect |
| 10. C22×D236 | C22 | semidirect |
| 13. #14273753 | C22 | direct (N × H) |
| 14. C2×#11745670 | C22 | semidirect |
| 15. C2×#11745669 | C22 | semidirect |
| 16. C2×#11745664 | C22 | semidirect |
| 17. C22×C59⋊C8 | C22 | semidirect |
| 22. C22×D4×C59 | C22 | semidirect |
| 33. C2×D4×C59 | C23 | semidirect |
| 41. #11745685 | C23 | semidirect |
| 43. C2×D236 | C23 | semidirect |
| 46. C2×Dic118 | C23 | semidirect |
| 47. #11745670 | C23 | semidirect |
| 48. #11745669 | C23 | semidirect |
| 49. #11745664 | C23 | semidirect |
| 50. C2×C59⋊C8 | C23 | semidirect |
| 71. D236 | C24 | semidirect |
| 74. Dic118 | C24 | semidirect |
| 75. C59⋊C8 | C24 | semidirect |
| 80. C22×C59 | AGL(1,ℤ/8) | semidirect |
| 92. C2×C59 | C2×AGL(1,ℤ/8) | semidirect |
| 96. C23×D4 | D59 | semidirect |
| 101. C59 | C22×AGL(1,ℤ/8) | semidirect |
| 111. C22×D4 | C2×D59 | semidirect |
| 135. C2×D4 | C22×D59 | semidirect |
| 177. C22 | #14273753 | direct (N × H) |
| 187. C2 | C2×#14273753 | direct (N × H) |