Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
244 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #21447651 | C2 | semidirect |
| 2. #21447638 | C2 | semidirect |
| 4. #21443888 | C2 | semidirect |
| 5. #21443775 | C2 | semidirect |
| 6. #21443735 | C2 | semidirect |
| 7. C61×D4⋊C16 | C2 | semidirect |
| 70. #11758185 | D8 | semidirect |
| 83. D244 | M32 | semidirect |
| 114. D4⋊C16 | D61 | semidirect |
| 136. C61 | #12038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447651 | 2 |
| #21447638 | 2 |
| C8×#11758199 | 2 |
| #21443888 | 2 |
| #21443775 | 2 |
| #21443735 | 2 |
| C61×D4⋊C16 | 2 |
| #12038 | 61 |