Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21446960 | C2 | semidirect |
| 3. #21446918 | C2 | semidirect |
| 4. #21443645 | C2 | semidirect |
| 5. #21443645 | C2 | semidirect |
| 73. C2×D4×C61 | Q16 | semidirect |
| 231. C61 | #7782 | semidirect |
| 284. C2×D4 | #11758202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446960 | 2 |
| #21446955 | 2 |
| #21446918 | 2 |
| #21443645 | 2 |
| #21443640 | 2 |
| C61×#2804 | 2 |
| #7782 | 61 |