Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #21445429 | C2 | semidirect |
| 5. #21443876 | C2 | semidirect |
| 6. #21443873 | C2 | semidirect |
| 7. C61×#1367 | C2 | semidirect |
| 104. #1367 | D61 | semidirect |
| 126. C61 | #12501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447967 | 2 |
| #21447957 | 2 |
| #21445429 | 2 |
| #21444705 | 2 |
| #21443876 | 2 |
| #21443873 | 2 |
| C61×#1367 | 2 |
| #12501 | 61 |