Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
890 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21447554 | C2 | semidirect |
| 3. #21447524 | C2 | semidirect |
| 4. #21447433 | C2 | semidirect |
| 5. C61×#1812 | C2 | semidirect |
| 11. #16840562 | C4 | semidirect |
| 14. C2×#14519717 | C22 | semidirect |
| 15. C22×#11758185 | C22 | semidirect |
| 21. C61×#427 | C22 | semidirect |
| 167. #1812 | D61 | semidirect |
| 184. #427 | C2×D61 | semidirect |
| 191. C61 | #12745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460593 | 2 |
| #21447554 | 2 |
| #21447524 | 2 |
| #21447433 | 2 |
| C61×#1812 | 2 |
| #12745 | 61 |