Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447727 | C2 | semidirect |
| 4. #21443883 | C2 | semidirect |
| 5. #21443799 | C2 | semidirect |
| 7. C8×C16×C61 | C2 | semidirect |
| 65. C16×C61 | SD16 | semidirect |
| 84. C8×C61 | M32 | semidirect |
| 108. C8×C16 | D61 | semidirect |
| 128. C61 | #12051 | semidirect |
| 173. C16 | #11758190 | semidirect |
| 192. C8 | #14519716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447727 | 2 |
| #21447652 | 2 |
| C8×#11758190 | 2 |
| #21443883 | 2 |
| #21443799 | 2 |
| #21443775 | 2 |
| C8×C16×C61 | 2 |
| #12051 | 61 |