Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21450818 | C2 | semidirect |
| 3. #21444488 | C2 | semidirect |
| 4. #21444314 | C2 | semidirect |
| 5. #21444214 | C2 | semidirect |
| 6. #21443720 | C2 | semidirect |
| 7. C61×#3037 | C2 | semidirect |
| 90. C2×Q8×C61 | D8 | semidirect |
| 221. #3037 | D61 | semidirect |
| 257. C61 | #10242 | semidirect |
| 317. C2×Q8 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456734 | 2 |
| #21450818 | 2 |
| #21444488 | 2 |
| #21444314 | 2 |
| #21444214 | 2 |
| #21443720 | 2 |
| C61×#3037 | 2 |
| #10242 | 61 |