Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1006 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 459 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 |
|---|---|---|
| 27. C4×C8×C61 | Q8 | semidirect |
| 57. C8×C61 | C4⋊Q8 | semidirect |
| 65. C4×C61 | #500 | semidirect |
| 85. C61 | #33312 | semidirect |
| 98. C4×C8 | Dic122 | semidirect |
| 129. C8 | #14519777 | semidirect |
| 137. C4 | #16840167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840167 | 2 |
| #21454217 | 2 |
| #21445979 | 2 |
| C42×C8×C61 | 2 |
| #33312 | 61 |