Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
878 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 239 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. #21445437 | C2 | semidirect |
| 4. #21445436 | C2 | semidirect |
| 5. #21445435 | C2 | semidirect |
| 7. C61×#1713 | C2 | semidirect |
| 67. C8×D61 | Q16 | semidirect |
| 82. C8×C61 | C2×Q16 | semidirect |
| 84. #92418 | C2×Q16 | semidirect |
| 100. #1713 | D61 | direct (N × H) |
| 104. D61 | #1713 | direct (N × H) |
| 121. C61 | C2×#1713 | semidirect |
| 182. C8 | Q16×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D61 | 2 |
| #494×D61 | 2 |
| #21445437 | 2 |
| #21445436 | 2 |
| #21445435 | 2 |
| C82×D61 | 2 |
| C61×#1713 | 2 |
| C2×#1713 | 61 |