Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
242 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #21447652 | C2 | semidirect |
| 3. #21443888 | C2 | semidirect |
| 4. D4⋊#11758185 | C2 | semidirect |
| 5. #21443773 | C2 | semidirect |
| 6. C16×#92418 | C2 | semidirect |
| 7. C61×#2169 | C2 | semidirect |
| 68. C16×C61 | D8 | semidirect |
| 93. #92418 | M32 | semidirect |
| 110. #2169 | D61 | semidirect |
| 136. C61 | #12039 | semidirect |
| 184. C16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447652 | 2 |
| C8×#11758199 | 2 |
| #21443888 | 2 |
| D4⋊#11758185 | 2 |
| #21443773 | 2 |
| C16×#92418 | 2 |
| C61×#2169 | 2 |
| #12039 | 61 |