Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
206 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 62. C16×C59 | Q16 | semidirect |
| 120. C59 | #12053 | semidirect |
| 162. C16 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic118 | 2 |
| C8×#11745672 | 2 |
| #21422165 | 2 |
| Q8⋊(C59⋊C16) | 2 |
| #21422074 | 2 |
| #21422012 | 2 |
| C59×#2183 | 2 |
| #12053 | 59 |