Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21447961 | C2 | semidirect |
| 4. #21443883 | C2 | semidirect |
| 5. #21443875 | C2 | semidirect |
| 7. C8×Q16×C61 | C2 | semidirect |
| 51. Q16×C61 | SD16 | semidirect |
| 91. C8×C61 | SD32 | semidirect |
| 110. C8×Q16 | D61 | semidirect |
| 133. C61 | #12417 | semidirect |
| 162. Q16 | #11758190 | semidirect |
| 202. C8 | #14519720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447961 | 2 |
| #21447859 | 2 |
| #21445411 | 2 |
| #21443883 | 2 |
| #21443875 | 2 |
| #21443864 | 2 |
| C8×Q16×C61 | 2 |
| #12417 | 61 |