Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21448069 | C2 | semidirect |
| 2. #21448068 | C2 | semidirect |
| 3. #21445433 | C2 | semidirect |
| 4. C16×#92418 | C2 | semidirect |
| 5. C61×#2246 | C2 | semidirect |
| 42. C16×C61 | D8 | semidirect |
| 43. #11758185 | D8 | semidirect |
| 56. #92418 | D16 | semidirect |
| 68. #2246 | D61 | semidirect |
| 84. C61 | #12515 | semidirect |
| 113. C16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448069 | 2 |
| #21448068 | 2 |
| #21445433 | 2 |
| C16×#92418 | 2 |
| C61×#2246 | 2 |
| #12515 | 61 |