Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21424233 | C2 | semidirect |
| 3. #21422548 | C2 | semidirect |
| 4. #21422547 | C2 | semidirect |
| 5. #21422546 | C2 | semidirect |
| 6. C2×#16837123 | C2 | semidirect |
| 7. C59×#1492 | C2 | semidirect |
| 173. #1492 | D59 | semidirect |
| 200. C59 | #9860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434522 | 2 |
| #21424233 | 2 |
| #21422548 | 2 |
| #21422547 | 2 |
| #21422546 | 2 |
| C2×#16837123 | 2 |
| C59×#1492 | 2 |
| #9860 | 59 |