Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊#92418 | C2 | semidirect |
| 2. #21444595 | C2 | semidirect |
| 5. #21443714 | C2 | semidirect |
| 6. #21443652 | C2 | semidirect |
| 15. #16839508 | C4 | semidirect |
| 16. #16839506 | C4 | semidirect |
| 178. C61 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#92418 | 2 |
| #21444595 | 2 |
| #21444468 | 2 |
| #21444218 | 2 |
| #21443714 | 2 |
| #21443652 | 2 |
| C61×#1962 | 2 |
| #9577 | 61 |