Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21447652 | C2 | semidirect |
| 2. #21445171 | C2 | semidirect |
| 3. #21443893 | C2 | semidirect |
| 4. #21443865 | C2 | semidirect |
| 5. C61×#2246 | C2 | semidirect |
| 53. C16×C61 | D8 | semidirect |
| 87. #2246 | D61 | semidirect |
| 108. C61 | #12433 | semidirect |
| 146. C16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447652 | 2 |
| #21445171 | 2 |
| #21443893 | 2 |
| #21443865 | 2 |
| C61×#2246 | 2 |
| #12433 | 61 |