Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21448046 | C2 | semidirect |
| 4. #21443892 | C2 | semidirect |
| 5. #21443875 | C2 | semidirect |
| 6. #21443868 | C2 | semidirect |
| 129. C61 | #12470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448046 | 2 |
| D4×#11758185 | 2 |
| #21445208 | 2 |
| #21443892 | 2 |
| #21443875 | 2 |
| #21443868 | 2 |
| C61×#1669 | 2 |
| #12470 | 61 |