Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21448068 | C2 | semidirect |
| 2. #21447859 | C2 | semidirect |
| 3. #21445174 | C2 | semidirect |
| 4. #21443865 | C2 | semidirect |
| 5. #21443783 | C2 | semidirect |
| 6. D4⋊#11758185 | C2 | semidirect |
| 7. C61×#3287 | C2 | semidirect |
| 71. Q16×C61 | D8 | semidirect |
| 147. #3287 | D61 | semidirect |
| 177. C61 | #12317 | semidirect |
| 224. Q16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448068 | 2 |
| #21447859 | 2 |
| #21445174 | 2 |
| #21443865 | 2 |
| #21443783 | 2 |
| D4⋊#11758185 | 2 |
| C61×#3287 | 2 |
| #12317 | 61 |