Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
220 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21444715 | C2 | semidirect |
| 4. #21443890 | C2 | semidirect |
| 5. #21443784 | C2 | semidirect |
| 6. #21443735 | C2 | semidirect |
| 67. #11758185 | M16 | semidirect |
| 128. C61 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519721 | 2 |
| #21444715 | 2 |
| #21444704 | 2 |
| #21443890 | 2 |
| #21443784 | 2 |
| #21443735 | 2 |
| C61×#1331 | 2 |
| #12084 | 61 |