Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 4. #21443893 | C2 | semidirect |
| 5. #21443892 | C2 | semidirect |
| 6. #21443890 | C2 | semidirect |
| 7. C61×#1371 | C2 | semidirect |
| 64. C16×C61 | M16 | semidirect |
| 66. #11758185 | M16 | semidirect |
| 107. #1371 | D61 | semidirect |
| 127. C61 | #12025 | semidirect |
| 171. C16 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519716 | 2 |
| #21444581 | 2 |
| #21444576 | 2 |
| #21443893 | 2 |
| #21443892 | 2 |
| #21443890 | 2 |
| C61×#1371 | 2 |
| #12025 | 61 |