Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 1. #21448092 | C2 | semidirect |
| 3. #21448044 | C2 | semidirect |
| 4. #21448042 | C2 | semidirect |
| 5. #21445411 | C2 | semidirect |
| 6. C8×#11758185 | C2 | semidirect |
| 7. C61×#1706 | C2 | semidirect |
| 69. #11758185 | SD16 | semidirect |
| 88. C8×C61 | D16 | semidirect |
| 110. #1706 | D61 | semidirect |
| 132. C61 | #12503 | semidirect |
| 198. C8 | #14519718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448092 | 2 |
| #21448068 | 2 |
| #21448044 | 2 |
| #21448042 | 2 |
| #21445411 | 2 |
| C8×#11758185 | 2 |
| C61×#1706 | 2 |
| #12503 | 61 |