Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #21443790 | C2 | semidirect |
| 5. #21443789 | C2 | semidirect |
| 6. #21443788 | C2 | semidirect |
| 7. C61×#1334 | C2 | semidirect |
| 73. Q16×C61 | M16 | semidirect |
| 97. Dic244 | M16 | semidirect |
| 155. #1334 | D61 | semidirect |
| 179. C61 | #11664 | semidirect |
| 229. Q16 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D61 | 2 |
| #21447620 | 2 |
| #21444573 | 2 |
| #21443790 | 2 |
| #21443789 | 2 |
| #21443788 | 2 |
| C61×#1334 | 2 |
| #11664 | 61 |