Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
644 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #21461931 | C2 | semidirect |
| 4. #21461930 | C2 | semidirect |
| 5. #21460653 | C2 | semidirect |
| 6. #21460653 | C2 | semidirect |
| 25. #16839506 | C4 | semidirect |
| 26. #16839505 | C4 | semidirect |
| 27. #16839505 | C4 | semidirect |
| 28. C61×#331 | C4 | semidirect |
| 64. C4⋊#92418 | C2×C4 | semidirect |
| 65. C4⋊#92418 | C2×C4 | semidirect |
| 69. C4⋊C8×C61 | C2×C4 | semidirect |
| 70. C4⋊C8×C61 | C2×C4 | semidirect |
| 267. #331 | #6923 | semidirect |
| 268. C61 | #8921 | semidirect |
| 304. C4⋊C8 | C2×#6923 | semidirect |
| 305. C4⋊C8 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462349 | 2 |
| #21461947 | 2 |
| #21461931 | 2 |
| #21461930 | 2 |
| #21460653 | 2 |
| #331×D61 | 2 |
| #8921 | 61 |