Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
486 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. C2×#16840652 | C2 | semidirect |
| 4. #21461626 | C2 | semidirect |
| 5. #21460890 | C2 | semidirect |
| 6. #21460884 | C2 | semidirect |
| 11. #16840803 | C4 | semidirect |
| 17. #16840680 | C4 | semidirect |
| 23. #16839564 | C4 | semidirect |
| 24. #16839563 | C4 | semidirect |
| 25. #16839562 | C4 | semidirect |
| 26. C61×#357 | C4 | semidirect |
| 36. #14519852 | C2×C4 | semidirect |
| 39. #14519847 | C2×C4 | semidirect |
| 58. C2×#11758185 | C2×C4 | semidirect |
| 59. #14519711 | C2×C4 | semidirect |
| 62. C2×C16×C61 | C2×C4 | semidirect |
| 63. #107×C61 | C2×C4 | semidirect |
| 198. #357 | #6923 | semidirect |
| 201. C61 | #12647 | semidirect |
| 226. C2×C16 | C2×#6923 | semidirect |
| 230. #107 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840803 | 2 |
| C2×#16840680 | 2 |
| C2×#16840652 | 2 |
| #21461626 | 2 |
| #21460890 | 2 |
| #21460884 | 2 |
| #21447533 | 2 |
| #12647 | 61 |