Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21424927 | C2 | semidirect |
| 3. #21422582 | C2 | semidirect |
| 4. #21422564 | C2 | semidirect |
| 5. #21421988 | C2 | semidirect |
| 6. #21421985 | C2 | semidirect |
| 7. C59×#2995 | C2 | semidirect |
| 9. #16837812 | C4 | semidirect |
| 10. #16837792 | C4 | semidirect |
| 11. #16837768 | C4 | semidirect |
| 12. #16837761 | C4 | semidirect |
| 211. #2995 | D59 | semidirect |
| 250. C59 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434692 | 2 |
| #21424927 | 2 |
| #21422582 | 2 |
| #21422564 | 2 |
| #21421988 | 2 |
| #21421985 | 2 |
| C59×#2995 | 2 |
| #8997 | 59 |