Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
946 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 192 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. #21462579 | C2 | semidirect |
| 2. #21461979 | C2 | semidirect |
| 4. #21461825 | C2 | semidirect |
| 5. #21461621 | C2 | semidirect |
| 22. #16840136 | C4 | semidirect |
| 23. #16840135 | C4 | semidirect |
| 24. #16840134 | C4 | semidirect |
| 25. #16840133 | C4 | semidirect |
| 27. C61×#492 | C4 | semidirect |
| 36. #14519846 | D4 | semidirect |
| 37. #14519845 | D4 | semidirect |
| 47. C2×#11758190 | C2×C4 | semidirect |
| 48. C2×#11758200 | C2×C4 | semidirect |
| 49. C2×#11758201 | C2×C4 | semidirect |
| 55. #14519777 | C2×C4 | semidirect |
| 57. #14519775 | C2×C4 | semidirect |
| 63. C4×#92418 | C2×C4 | semidirect |
| 64. C8×Dic61 | C2×C4 | semidirect |
| 65. C2×SD16×C61 | C2×C4 | semidirect |
| 66. C4⋊Q8×C61 | C2×C4 | semidirect |
| 68. C4×C8×C61 | C2×C4 | semidirect |
| 189. #492 | #6923 | semidirect |
| 201. C61 | #23198 | semidirect |
| 212. C2×SD16 | C2×#6923 | semidirect |
| 218. C4⋊Q8 | C2×#6923 | semidirect |
| 242. C4×C8 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462579 | 2 |
| #21461979 | 2 |
| #21461826 | 2 |
| #21461825 | 2 |
| #21461621 | 2 |
| #492×D61 | 2 |
| #23198 | 61 |