Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#16839883 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. C2×#16839571 | C2 | semidirect |
| 5. #21446693 | C2 | semidirect |
| 6. #21443898 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 13. C2×#14519722 | C4 | semidirect |
| 14. C2×D976 | C4 | semidirect |
| 104. Dic244 | C22⋊C4 | semidirect |
| 110. D488 | C22⋊C4 | semidirect |
| 177. #1383 | D61 | semidirect |
| 204. C61 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840200 | 2 |
| C2×#16839883 | 2 |
| C2×#16839574 | 2 |
| C2×#16839571 | 2 |
| #21446693 | 2 |
| #21443898 | 2 |
| C61×#1383 | 2 |
| #13040 | 61 |