Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
384 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #21425870 | C2 | semidirect |
| 3. C2×#16837217 | C2 | semidirect |
| 4. #21425817 | C2 | semidirect |
| 7. C59×#1388 | C2 | semidirect |
| 160. #1388 | D59 | semidirect |
| 183. C59 | #13403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837678 | 2 |
| #21425870 | 2 |
| C2×#16837217 | 2 |
| #21425817 | 2 |
| #21425716 | 2 |
| #21424151 | 2 |
| C59×#1388 | 2 |
| #13403 | 59 |