Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
178 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21447603 | C2 | semidirect |
| 2. #21444020 | C2 | semidirect |
| 3. #21444018 | C2 | semidirect |
| 4. #21443997 | C2 | semidirect |
| 5. #21443997 | C2 | semidirect |
| 6. C22⋊#14519683 | C2 | semidirect |
| 106. C61 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447603 | 2 |
| #21444020 | 2 |
| #21444018 | 2 |
| #21443997 | 2 |
| C22⋊#14519683 | 2 |
| C61×#2215 | 2 |
| #13713 | 61 |