Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 82 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. #21462167 | C2 | semidirect |
| 4. #21461926 | C2 | semidirect |
| 5. #21460886 | C2 | semidirect |
| 6. #21460862 | C2 | semidirect |
| 27. #16839573 | C4 | semidirect |
| 28. #16839572 | C4 | semidirect |
| 29. #16839571 | C4 | semidirect |
| 30. C61×#360 | C4 | semidirect |
| 70. #14519717 | C2×C4 | semidirect |
| 74. #14519709 | C2×C4 | semidirect |
| 76. M32×C61 | C2×C4 | semidirect |
| 77. #106×C61 | C2×C4 | semidirect |
| 227. #360 | #6923 | semidirect |
| 229. C61 | #12951 | semidirect |
| 258. M32 | C2×#6923 | semidirect |
| 268. #106 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×#6923 | 2 |
| #21462167 | 2 |
| #21462147 | 2 |
| #21461926 | 2 |
| #21460886 | 2 |
| #21460862 | 2 |
| #21447553 | 2 |
| #12951 | 61 |