Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 102 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. #21461734 | C2 | semidirect |
| 3. #21461370 | C2 | semidirect |
| 5. #21460665 | C2 | semidirect |
| 6. #21460647 | C2 | semidirect |
| 91. M16×C61 | M16 | semidirect |
| 98. C42×C61 | M16 | semidirect |
| 216. C61 | #8842 | semidirect |
| 274. M16 | #11758213 | semidirect |
| 304. C42 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462740 | 2 |
| #21461734 | 2 |
| #21461370 | 2 |
| #21461116 | 2 |
| #21460665 | 2 |
| #21460647 | 2 |
| #21445623 | 2 |
| #8842 | 61 |