Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 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. #21448099 | C2 | semidirect |
| 3. #21445210 | C2 | semidirect |
| 4. #21443876 | C2 | semidirect |
| 5. #21443797 | C2 | semidirect |
| 59. D8×C61 | Q16 | semidirect |
| 147. C61 | #12407 | semidirect |
| 183. D8 | #11758202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458684 | 2 |
| #21448099 | 2 |
| #21445210 | 2 |
| #21443876 | 2 |
| #21443797 | 2 |
| #21443780 | 2 |
| C61×#2224 | 2 |
| #12407 | 61 |