Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
542 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 125 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. #21444574 | C2 | semidirect |
| 4. #21444500 | C2 | semidirect |
| 6. M16×#92418 | C2 | semidirect |
| 7. C61×#1997 | C2 | semidirect |
| 81. M16×C61 | SD16 | semidirect |
| 131. #92418 | #100 | semidirect |
| 150. #1997 | D61 | semidirect |
| 179. C61 | #9793 | semidirect |
| 238. M16 | #11758201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840136 | 2 |
| #21446659 | 2 |
| #21444574 | 2 |
| #21444500 | 2 |
| #21444488 | 2 |
| M16×#92418 | 2 |
| C61×#1997 | 2 |
| #9793 | 61 |