Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 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. #21448076 | C2 | semidirect |
| 2. #21448075 | C2 | semidirect |
| 3. #21448074 | C2 | semidirect |
| 4. #21445435 | C2 | semidirect |
| 6. C16×#92418 | C2 | semidirect |
| 7. C61×#2248 | C2 | semidirect |
| 64. C16×C61 | D8 | semidirect |
| 65. #11758185 | D8 | semidirect |
| 84. #92418 | SD32 | semidirect |
| 99. #2248 | D61 | semidirect |
| 120. C61 | #12517 | semidirect |
| 165. C16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448076 | 2 |
| #21448075 | 2 |
| #21448074 | 2 |
| #21445435 | 2 |
| #21445433 | 2 |
| C16×#92418 | 2 |
| C61×#2248 | 2 |
| #12517 | 61 |