Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 2. #21454407 | C2 | semidirect |
| 3. #21447556 | C2 | semidirect |
| 4. #21447554 | C2 | semidirect |
| 5. C2×#16839543 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 7. C61×#1384 | C2 | semidirect |
| 13. #16840021 | C4 | semidirect |
| 14. #16840016 | C4 | semidirect |
| 33. C2×Dic244 | C2×C4 | semidirect |
| 35. C2×D488 | C2×C4 | semidirect |
| 60. #14519709 | D4 | semidirect |
| 72. #106×C61 | C2×C4 | semidirect |
| 73. #106×C61 | D4 | semidirect |
| 193. #1384 | D61 | semidirect |
| 219. C61 | #13008 | semidirect |
| 263. #106 | C4×D61 | semidirect |
| 264. #106 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455429 | 2 |
| #21454407 | 2 |
| #21447556 | 2 |
| #21447554 | 2 |
| C2×#16839543 | 2 |
| #21443920 | 2 |
| C61×#1384 | 2 |
| #13008 | 61 |