Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #21448086 | C2 | semidirect |
| 2. #21447859 | C2 | semidirect |
| 3. #21445298 | C2 | semidirect |
| 4. #21443862 | C2 | semidirect |
| 5. #21443789 | C2 | semidirect |
| 6. #21443777 | C2 | semidirect |
| 7. C61×#3277 | C2 | semidirect |
| 85. Q16×C61 | D8 | semidirect |
| 167. #3277 | D61 | semidirect |
| 199. C61 | #12325 | semidirect |
| 258. Q16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448086 | 2 |
| #21447859 | 2 |
| #21445298 | 2 |
| #21443862 | 2 |
| #21443789 | 2 |
| #21443777 | 2 |
| C61×#3277 | 2 |
| #12325 | 61 |