Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
394 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
| 3. C2×#16840687 | C2 | semidirect |
| 5. #21460891 | C2 | semidirect |
| 6. #21460887 | C2 | semidirect |
| 25. #16839547 | C4 | semidirect |
| 26. #16839546 | C4 | semidirect |
| 27. #16839545 | C4 | semidirect |
| 28. C61×#350 | C4 | semidirect |
| 61. #14519717 | C2×C4 | semidirect |
| 65. C2×#11758185 | C2×C4 | semidirect |
| 68. M32×C61 | C2×C4 | semidirect |
| 69. C2×C16×C61 | C2×C4 | semidirect |
| 206. #350 | #6923 | semidirect |
| 208. C61 | #12934 | semidirect |
| 233. M32 | C2×#6923 | semidirect |
| 236. C2×C16 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462473 | 2 |
| #21462167 | 2 |
| C2×#16840687 | 2 |
| #21461705 | 2 |
| #21460891 | 2 |
| #21460887 | 2 |
| #21447445 | 2 |
| #12934 | 61 |