Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447616 | C2 | semidirect |
| 3. #21444576 | C2 | semidirect |
| 4. #21443783 | C2 | semidirect |
| 5. #21443781 | C2 | semidirect |
| 6. #21443779 | C2 | semidirect |
| 7. C61×#1332 | C2 | semidirect |
| 74. Q16×C61 | M16 | semidirect |
| 97. D488 | M16 | semidirect |
| 159. #1332 | D61 | semidirect |
| 186. C61 | #11660 | semidirect |
| 234. Q16 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519800 | 2 |
| #21447616 | 2 |
| #21444576 | 2 |
| #21443783 | 2 |
| #21443781 | 2 |
| #21443779 | 2 |
| C61×#1332 | 2 |
| #11660 | 61 |