Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
706 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 219 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. #21445436 | C2 | semidirect |
| 4. #21445428 | C2 | semidirect |
| 5. #21445414 | C2 | semidirect |
| 60. C2×C8×C61 | Q16 | semidirect |
| 136. C61 | #19604 | semidirect |
| 172. C2×C8 | #11758202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456401 | 2 |
| #21456333 | 2 |
| #21445436 | 2 |
| #21445428 | 2 |
| #21445414 | 2 |
| C2×C8×#92418 | 2 |
| C61×#3160 | 2 |
| #19604 | 61 |