Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
562 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 562 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 |
|---|---|---|
| 2. C2×#16837721 | C2 | semidirect |
| 3. C2×#16837716 | C2 | semidirect |
| 4. #21424174 | C2 | semidirect |
| 5. #21422455 | C2 | semidirect |
| 6. #21422455 | C2 | semidirect |
| 7. C59×#1298 | C2 | semidirect |
| 201. #1298 | D59 | semidirect |
| 233. C59 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434896 | 2 |
| C2×#16837721 | 2 |
| C2×#16837716 | 2 |
| #21424174 | 2 |
| #21422455 | 2 |
| C59×#1298 | 2 |
| #9992 | 59 |