Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
594 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21446656 | C2 | semidirect |
| 3. #21446654 | C2 | semidirect |
| 4. #21445842 | C2 | semidirect |
| 5. #21445598 | C2 | semidirect |
| 6. #21444388 | C2 | semidirect |
| 7. C61×#1519 | C2 | semidirect |
| 8. C22×#11758199 | C4 | semidirect |
| 15. C2×#14519710 | C4 | semidirect |
| 17. C2×#14519698 | C4 | semidirect |
| 18. C2×#14519697 | C4 | semidirect |
| 202. #92418 | #99 | semidirect |
| 241. #1519 | D61 | semidirect |
| 274. C61 | #9785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839996 | 2 |
| #21446656 | 2 |
| #21446654 | 2 |
| #21445842 | 2 |
| #21445598 | 2 |
| #21444388 | 2 |
| C61×#1519 | 2 |
| #9785 | 61 |