Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #21443784 | C2 | semidirect |
| 5. #21443783 | C2 | semidirect |
| 6. #21443782 | C2 | semidirect |
| 7. C61×#1332 | C2 | semidirect |
| 73. Q16×C61 | M16 | semidirect |
| 97. Dic244 | M16 | semidirect |
| 157. #1332 | D61 | semidirect |
| 181. C61 | #11658 | semidirect |
| 231. Q16 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D61 | 2 |
| #21447616 | 2 |
| #21444576 | 2 |
| #21443784 | 2 |
| #21443783 | 2 |
| #21443782 | 2 |
| C61×#1332 | 2 |
| #11658 | 61 |