Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1124 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 211 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. C2×#16840203 | C2 | semidirect |
| 3. #21447753 | C2 | semidirect |
| 4. #21447736 | C2 | semidirect |
| 5. #21447539 | C2 | semidirect |
| 6. #21447430 | C2 | semidirect |
| 7. C23×Q16×C61 | C2 | semidirect |
| 11. C2×#14519723 | C22 | semidirect |
| 12. C2×#14519720 | C22 | semidirect |
| 19. #16839566 | C22 | semidirect |
| 61. C2×Q16×C61 | D4 | semidirect |
| 154. C22×C61 | #510 | semidirect |
| 165. C23×Q16 | D61 | semidirect |
| 197. C61 | #33518 | semidirect |
| 215. C2×Q16 | C22⋊D61 | semidirect |
| 325. C22 | #16840203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840203 | 2 |
| #21455400 | 2 |
| #21447753 | 2 |
| #21447736 | 2 |
| #21447539 | 2 |
| #21447430 | 2 |
| C23×Q16×C61 | 2 |
| #33518 | 61 |