Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
522 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21454620 | C2 | semidirect |
| 3. #21447536 | C2 | semidirect |
| 4. #21446693 | C2 | semidirect |
| 5. #21443926 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C2×C61×#360 | C2 | semidirect |
| 11. #16840197 | C4 | semidirect |
| 34. C2×D488 | C2×C4 | semidirect |
| 47. #14519717 | C2×C4 | semidirect |
| 91. Q16×C61 | C22⋊C4 | semidirect |
| 95. D8×C61 | C22⋊C4 | semidirect |
| 181. C2×#360 | D61 | semidirect |
| 212. C61 | #13025 | semidirect |
| 276. Q16 | #11758198 | semidirect |
| 284. D8 | #11758198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| #21454620 | 2 |
| #21447536 | 2 |
| #21446693 | 2 |
| #21443926 | 2 |
| #21443902 | 2 |
| C2×C61×#360 | 2 |
| #13025 | 61 |