Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 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. #21447556 | C2 | semidirect |
| 4. #21447554 | C2 | semidirect |
| 5. #21445862 | C2 | semidirect |
| 6. #21443926 | C2 | semidirect |
| 7. C61×#1386 | C2 | semidirect |
| 15. #16840021 | C4 | semidirect |
| 16. #16840016 | C4 | semidirect |
| 50. #14519717 | D4 | semidirect |
| 63. M32×C61 | D4 | semidirect |
| 182. #1386 | D61 | semidirect |
| 208. C61 | #13077 | semidirect |
| 238. M32 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458921 | 2 |
| #21455482 | 2 |
| #21447556 | 2 |
| #21447554 | 2 |
| #21445862 | 2 |
| #21443926 | 2 |
| C61×#1386 | 2 |
| #13077 | 61 |