Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 84 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. #21462171 | C2 | semidirect |
| 4. #21461925 | C2 | semidirect |
| 5. #21460892 | C2 | semidirect |
| 6. #21460865 | C2 | semidirect |
| 27. #16839573 | C4 | semidirect |
| 28. #16839572 | C4 | semidirect |
| 29. #16839571 | C4 | semidirect |
| 30. C61×#360 | C4 | semidirect |
| 70. #14519717 | C2×C4 | semidirect |
| 73. #14519709 | C2×C4 | semidirect |
| 76. M32×C61 | C2×C4 | semidirect |
| 77. #106×C61 | C2×C4 | semidirect |
| 113. Q16×C61 | C4⋊C4 | semidirect |
| 115. D8×C61 | C4⋊C4 | semidirect |
| 125. Dic244 | C4⋊C4 | semidirect |
| 126. D488 | C4⋊C4 | semidirect |
| 234. #360 | #6923 | semidirect |
| 238. C61 | #12943 | semidirect |
| 268. M32 | C2×#6923 | semidirect |
| 278. #106 | C2×#6923 | semidirect |
| 305. Q16 | C4⋊#6923 | semidirect |
| 312. D8 | C4⋊#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462573 | 2 |
| #21462171 | 2 |
| #21462127 | 2 |
| #21461925 | 2 |
| #21460892 | 2 |
| #21460865 | 2 |
| #360×D61 | 2 |
| #12943 | 61 |