Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16840029 | C2 | semidirect |
| 2. #21455485 | C2 | semidirect |
| 3. C2×#16839569 | C2 | semidirect |
| 4. C2×#16839563 | C2 | semidirect |
| 5. C2×#16839547 | C2 | semidirect |
| 6. #21443928 | C2 | semidirect |
| 7. C2×C61×#509 | C2 | semidirect |
| 54. #14519713 | D4 | semidirect |
| 74. C2×D8×C61 | D4 | semidirect |
| 79. M32×C61 | D4 | semidirect |
| 211. C2×#509 | D61 | semidirect |
| 249. C61 | #13307 | semidirect |
| 269. C2×D8 | C22⋊D61 | semidirect |
| 288. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840029 | 2 |
| #21455485 | 2 |
| C2×#16839569 | 2 |
| C2×#16839563 | 2 |
| C2×#16839547 | 2 |
| #21443928 | 2 |
| C2×C61×#509 | 2 |
| #13307 | 61 |