Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21447608 | C2 | semidirect |
| 5. #21446563 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C61×#1386 | C2 | semidirect |
| 21. #16839571 | C4 | semidirect |
| 49. #14519717 | C2×C4 | semidirect |
| 70. #106×C61 | C2×C4 | semidirect |
| 113. Dic244 | C4⋊C4 | semidirect |
| 115. D488 | C4⋊C4 | semidirect |
| 181. #1386 | D61 | semidirect |
| 209. C61 | #12943 | semidirect |
| 245. #106 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454619 | 2 |
| #21447608 | 2 |
| C2×#16839571 | 2 |
| #21447532 | 2 |
| #21446563 | 2 |
| #21443902 | 2 |
| C61×#1386 | 2 |
| #12943 | 61 |