Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
494 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21446663 | C2 | semidirect |
| 4. #21444578 | C2 | semidirect |
| 5. #21444490 | C2 | semidirect |
| 7. C8×M16×C61 | C2 | semidirect |
| 155. C8×M16 | D61 | semidirect |
| 179. C61 | #9796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840109 | 2 |
| #21446663 | 2 |
| #21446659 | 2 |
| #21444578 | 2 |
| #21444490 | 2 |
| #21444486 | 2 |
| C8×M16×C61 | 2 |
| #9796 | 61 |