Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21458953 | C2 | semidirect |
| 2. #21455540 | C2 | semidirect |
| 3. #21455477 | C2 | semidirect |
| 4. C2×#16839573 | C2 | semidirect |
| 5. #21447448 | C2 | semidirect |
| 6. #21443919 | C2 | semidirect |
| 7. C61×#2143 | C2 | semidirect |
| 44. C2×Dic244 | D4 | semidirect |
| 46. C2×D488 | D4 | semidirect |
| 66. C2×#11758185 | D4 | semidirect |
| 87. #108×C61 | D4 | semidirect |
| 224. #2143 | D61 | semidirect |
| 259. C61 | #13318 | semidirect |
| 308. #108 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| #21455540 | 2 |
| #21455477 | 2 |
| C2×#16839573 | 2 |
| #21447448 | 2 |
| #21443919 | 2 |
| C61×#2143 | 2 |
| #13318 | 61 |