Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
224 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #21443890 | C2 | semidirect |
| 4. #21443783 | C2 | semidirect |
| 6. #21443737 | C2 | semidirect |
| 7. C8×Q16×C61 | C2 | semidirect |
| 48. Q16×C61 | M16 | semidirect |
| 104. C8×Q16 | D61 | semidirect |
| 128. C61 | #12075 | semidirect |
| 154. Q16 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519720 | 2 |
| #21444705 | 2 |
| #21443890 | 2 |
| #21443783 | 2 |
| #21443779 | 2 |
| #21443737 | 2 |
| C8×Q16×C61 | 2 |
| #12075 | 61 |