Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
654 conjugacy classes of subgroups; only the 308 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 308 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 |
|---|---|---|
| 11. #92420⋊C8 | C4 | semidirect |
| 12. #16840603 | C4 | semidirect |
| 15. #16839484 | C4 | semidirect |
| 16. #16839483 | C4 | semidirect |
| 17. C61×#322 | C4 | semidirect |
| 26. C8×#6923 | C8 | semidirect |
| 64. #92420 | C4×C8 | semidirect |
| 66. C8×C61 | C4×C8 | semidirect |
| 68. #92418 | C4×C8 | semidirect |
| 73. #6923 | #322 | direct (N × H) |
| 97. #322 | #6923 | direct (N × H) |
| 98. C61 | C4×#322 | semidirect |
| 149. C8 | C8×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×#6923 | 2 |
| #21461015 | 2 |
| #21461013 | 2 |
| #322×D61 | 2 |
| C4×#322 | 61 |