Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×#14519712 | C2 | semidirect |
| 3. #21444411 | C2 | semidirect |
| 4. #21444410 | C2 | semidirect |
| 5. #21444235 | C2 | semidirect |
| 6. #21444100 | C2 | semidirect |
| 7. C61×#1484 | C2 | semidirect |
| 183. #1484 | D61 | semidirect |
| 214. C61 | #9724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456394 | 2 |
| C4×#14519712 | 2 |
| #21444411 | 2 |
| #21444410 | 2 |
| #21444235 | 2 |
| #21444100 | 2 |
| C61×#1484 | 2 |
| #9724 | 61 |