Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
5758 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 5758 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×#11758213 | C2 | semidirect |
| 2. C23×C4×#6923 | C2 | semidirect |
| 3. C22×#14519841 | C2 | direct (N × H) |
| 7. C22×#11758213 | C22 | semidirect |
| 10. C22×C4×#6923 | C22 | semidirect |
| 11. C2×#14519841 | C22 | direct (N × H) |
| 14. C22×#11758224 | C4 | semidirect |
| 16. C23×Dic122 | C4 | semidirect |
| 20. C23×D4×C61 | C4 | semidirect |
| 24. C2×#11758213 | C23 | semidirect |
| 27. C2×C4×#6923 | C23 | semidirect |
| 28. #14519841 | C23 | direct (N × H) |
| 33. C2×#11758224 | C2×C4 | semidirect |
| 36. C22×Dic122 | C2×C4 | semidirect |
| 49. C22×D4×C61 | C2×C4 | semidirect |
| 60. C2×D4×C61 | C22×C4 | semidirect |
| 73. #11758224 | C22×C4 | semidirect |
| 81. C2×Dic122 | C22×C4 | semidirect |
| 84. C4×#6923 | C24 | semidirect |
| 86. #11758213 | C24 | semidirect |
| 89. C23×C61 | #104 | semidirect |
| 98. D4×C61 | C23×C4 | semidirect |
| 114. Dic122 | C23×C4 | semidirect |
| 119. C22×C61 | C2×#104 | semidirect |
| 136. C2×C61 | C22×#104 | semidirect |
| 146. C23×D4 | #6923 | semidirect |
| 156. C61 | C23×#104 | semidirect |
| 169. C22×D4 | C2×#6923 | semidirect |
| 203. C2×D4 | C22×#6923 | semidirect |
| 229. C23 | #14519841 | direct (N × H) |
| 236. D4 | C23×#6923 | semidirect |
| 258. C22 | C2×#14519841 | direct (N × H) |
| 269. C2 | C22×#14519841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11758213 | 2 |
| C23×C4×#6923 | 2 |
| C22×#14519841 | 2 |
| C23×#11758224 | 2 |
| C23×#104 | 61 |