Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 207 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. #21443735 | C2 | semidirect |
| 4. C8×#11758185 | C2 | semidirect |
| 5. C8×C16×C61 | C2 | semidirect |
| 18. #14519716 | C8 | direct (N × H) |
| 38. C16×C61 | C2×C8 | semidirect |
| 39. #11758185 | C2×C8 | semidirect |
| 47. C8×C61 | M32 | semidirect |
| 63. C8×C16 | D61 | semidirect |
| 76. C61 | C8×M32 | semidirect |
| 101. C16 | C8×D61 | semidirect |
| 111. C8 | #14519716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519716 | 2 |
| C82×D61 | 2 |
| #21443735 | 2 |
| C8×#11758185 | 2 |
| C8×C16×C61 | 2 |
| C8×M32 | 61 |