Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
430 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #21447616 | C2 | semidirect |
| 3. #21444576 | C2 | semidirect |
| 4. #21443781 | C2 | semidirect |
| 5. #21443780 | C2 | semidirect |
| 6. #21443779 | C2 | semidirect |
| 7. C61×#1331 | C2 | semidirect |
| 21. C4×#11758185 | C22 | semidirect |
| 22. #16839515 | C22 | semidirect |
| 25. C4×C16×C61 | C22 | semidirect |
| 26. C61×#335 | C22 | semidirect |
| 79. D8×C61 | M16 | semidirect |
| 99. D488 | M16 | semidirect |
| 172. #1331 | D61 | semidirect |
| 194. C4×C16 | C2×D61 | semidirect |
| 197. #335 | C2×D61 | semidirect |
| 198. C61 | #11657 | semidirect |
| 254. D8 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D61 | 2 |
| #21447616 | 2 |
| #21444576 | 2 |
| #21443781 | 2 |
| #21443780 | 2 |
| #21443779 | 2 |
| C61×#1331 | 2 |
| #11657 | 61 |