Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21458921 | C2 | semidirect |
| 3. #21447536 | C2 | semidirect |
| 4. #21447534 | C2 | semidirect |
| 5. #21445862 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 7. C61×#1384 | C2 | semidirect |
| 15. #16840016 | C4 | semidirect |
| 49. C2×#11758185 | D4 | semidirect |
| 60. C2×C16×C61 | D4 | semidirect |
| 170. #1384 | D61 | semidirect |
| 195. C61 | #13074 | semidirect |
| 226. C2×C16 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458921 | 2 |
| #21455468 | 2 |
| #21447536 | 2 |
| #21447534 | 2 |
| #21445862 | 2 |
| #21443920 | 2 |
| C61×#1384 | 2 |
| #13074 | 61 |