Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
4830 conjugacy classes of subgroups; only the 763 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 763 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. #21444090 | C2 | semidirect |
| 4. #21444089 | C2 | semidirect |
| 5. C61×#1446 | C2 | semidirect |
| 8. C22×Q8×D61 | C4 | semidirect |
| 19. C22×Dic122 | C2×C4 | semidirect |
| 29. C22×C4×D61 | Q8 | semidirect |
| 33. C22×Q8×C61 | C2×C4 | semidirect |
| 49. C22×C4×C61 | C2×Q8 | semidirect |
| 55. C22×Dic61 | C2×Q8 | semidirect |
| 111. #1446 | D61 | direct (N × H) |
| 116. D61 | #1446 | direct (N × H) |
| 127. C61 | C2×#1446 | semidirect |
| 135. C22×Q8 | C4×D61 | semidirect |
| 177. C22×C4 | Q8×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×D61 | 2 |
| C2×#95×D61 | 2 |
| #21444090 | 2 |
| #21444089 | 2 |
| C61×#1446 | 2 |
| C2×#1446 | 61 |