Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
740 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21455612 | C2 | semidirect |
| 3. #21444487 | C2 | semidirect |
| 4. #21444318 | C2 | semidirect |
| 5. #21444209 | C2 | semidirect |
| 6. #21443721 | C2 | semidirect |
| 7. C61×#3208 | C2 | semidirect |
| 51. C4⋊#92418 | D4 | semidirect |
| 61. C4⋊Q8×C61 | D4 | semidirect |
| 62. C4⋊Q8×C61 | D4 | semidirect |
| 74. C4⋊C8×C61 | D4 | semidirect |
| 107. C2×D244 | SD16 | semidirect |
| 215. #3208 | D61 | semidirect |
| 252. C61 | #10246 | semidirect |
| 261. C4⋊Q8 | C22⋊D61 | semidirect |
| 262. C4⋊Q8 | C22⋊D61 | semidirect |
| 291. C4⋊C8 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455612 | 2 |
| #21450766 | 2 |
| #21444487 | 2 |
| #21444318 | 2 |
| #21444209 | 2 |
| #21443721 | 2 |
| C61×#3208 | 2 |
| #10246 | 61 |