Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. #21454201 | C2 | semidirect |
| 2. #21454186 | C2 | semidirect |
| 3. #21454134 | C2 | semidirect |
| 4. C4×#14519771 | C2 | semidirect |
| 6. #21448302 | C2 | semidirect |
| 7. C2×C43×C61 | C2 | semidirect |
| 65. C42×C61 | #41 | semidirect |
| 79. C2×C4×C61 | #126 | semidirect |
| 108. C2×C43 | D61 | semidirect |
| 130. C61 | #36641 | semidirect |
| 176. C42 | #11758222 | semidirect |
| 192. C2×C4 | #14519771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454201 | 2 |
| #21454186 | 2 |
| #21454134 | 2 |
| C4×#14519771 | 2 |
| #21448309 | 2 |
| #21448302 | 2 |
| C2×C43×C61 | 2 |
| #36641 | 61 |