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. #21447555 | C2 | semidirect |
| 4. #21445862 | C2 | semidirect |
| 5. #21443925 | C2 | semidirect |
| 6. #21443924 | C2 | semidirect |
| 7. C61×#2145 | C2 | semidirect |
| 14. #16840017 | C4 | semidirect |
| 15. #16840012 | C4 | semidirect |
| 43. #14519717 | D4 | semidirect |
| 65. M32×C61 | D4 | semidirect |
| 179. #2145 | D61 | semidirect |
| 208. C61 | #13077 | semidirect |
| 238. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458921 | 2 |
| #21455477 | 2 |
| #21447555 | 2 |
| #21445862 | 2 |
| #21443925 | 2 |
| #21443924 | 2 |
| C61×#2145 | 2 |
| #13077 | 61 |