Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
| 3. C2×#16840689 | C2 | semidirect |
| 5. #21460894 | C2 | semidirect |
| 6. #21460881 | C2 | semidirect |
| 25. #16839547 | C4 | semidirect |
| 26. #16839546 | C4 | semidirect |
| 27. #16839545 | C4 | semidirect |
| 28. C61×#350 | C4 | semidirect |
| 61. #14519717 | C2×C4 | semidirect |
| 63. C2×#11758185 | C2×C4 | semidirect |
| 68. M32×C61 | C2×C4 | semidirect |
| 69. C2×C16×C61 | C2×C4 | semidirect |
| 210. #350 | #6923 | semidirect |
| 212. C61 | #12926 | semidirect |
| 235. M32 | C2×#6923 | semidirect |
| 240. C2×C16 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462474 | 2 |
| #21462171 | 2 |
| C2×#16840689 | 2 |
| #21461708 | 2 |
| #21460894 | 2 |
| #21460881 | 2 |
| #350×D61 | 2 |
| #12926 | 61 |