Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21447592 | C2 | semidirect |
| 3. C2×#16839584 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 7. C61×#1386 | C2 | semidirect |
| 21. #16839547 | C4 | semidirect |
| 43. C2×#11758185 | C2×C4 | semidirect |
| 56. M32×C61 | C2×C4 | semidirect |
| 153. #1386 | D61 | semidirect |
| 178. C61 | #12934 | semidirect |
| 200. M32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454410 | 2 |
| #21447592 | 2 |
| C2×#16839584 | 2 |
| #21447448 | 2 |
| #21445870 | 2 |
| #21443920 | 2 |
| C61×#1386 | 2 |
| #12934 | 61 |