Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
442 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 2. #21448074 | C2 | semidirect |
| 3. #21447865 | C2 | semidirect |
| 4. #21445185 | C2 | semidirect |
| 5. #21443779 | C2 | semidirect |
| 6. #21443773 | C2 | semidirect |
| 7. C61×#1361 | C2 | semidirect |
| 12. #16840142 | C22 | semidirect |
| 20. C4×#11758185 | C22 | semidirect |
| 23. C61×C4⋊C16 | C22 | semidirect |
| 24. C61×#335 | C22 | semidirect |
| 118. D244 | SD32 | semidirect |
| 154. #1361 | D61 | semidirect |
| 175. C4⋊C16 | C2×D61 | semidirect |
| 178. #335 | C2×D61 | semidirect |
| 180. C61 | #12320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457494 | 2 |
| #21448074 | 2 |
| #21447865 | 2 |
| #21445185 | 2 |
| #21443779 | 2 |
| #21443773 | 2 |
| C61×#1361 | 2 |
| #12320 | 61 |