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×#14519842 | C2 | direct (N × H) |
| 7. C22×#11758213 | C22 | semidirect |
| 10. C22×C4×#6923 | C22 | semidirect |
| 11. C2×#14519842 | C22 | direct (N × H) |
| 14. C22×#11758226 | C4 | semidirect |
| 17. C23×D244 | C4 | semidirect |
| 20. C23×Q8×C61 | C4 | semidirect |
| 24. C2×#11758213 | C23 | semidirect |
| 27. C2×C4×#6923 | C23 | semidirect |
| 28. #14519842 | C23 | direct (N × H) |
| 34. C2×#11758226 | C2×C4 | semidirect |
| 39. C22×D244 | C2×C4 | semidirect |
| 48. C22×Q8×C61 | C2×C4 | semidirect |
| 60. C2×Q8×C61 | C22×C4 | semidirect |
| 69. #11758226 | C22×C4 | semidirect |
| 74. C2×D244 | C22×C4 | semidirect |
| 84. C4×#6923 | C24 | semidirect |
| 86. #11758213 | C24 | semidirect |
| 87. C23×C61 | #104 | semidirect |
| 98. Q8×C61 | C23×C4 | semidirect |
| 107. D244 | C23×C4 | semidirect |
| 117. C22×C61 | C2×#104 | semidirect |
| 135. C2×C61 | C22×#104 | semidirect |
| 144. C23×Q8 | #6923 | semidirect |
| 156. C61 | C23×#104 | semidirect |
| 165. C22×Q8 | C2×#6923 | semidirect |
| 199. C2×Q8 | C22×#6923 | semidirect |
| 229. C23 | #14519842 | direct (N × H) |
| 232. Q8 | C23×#6923 | semidirect |
| 258. C22 | C2×#14519842 | direct (N × H) |
| 269. C2 | C22×#14519842 | 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×#14519842 | 2 |
| C23×#11758226 | 2 |
| C23×#104 | 61 |