Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21425016 | C2 | semidirect |
| 3. #21425014 | C2 | semidirect |
| 4. C4×#14273658 | C2 | semidirect |
| 5. #21422592 | C2 | semidirect |
| 6. #21422386 | C2 | semidirect |
| 7. C59×#1502 | C2 | semidirect |
| 9. #16837805 | C4 | semidirect |
| 10. #16837778 | C4 | semidirect |
| 11. #16837750 | C4 | semidirect |
| 12. #16837748 | C4 | semidirect |
| 171. C59⋊C8 | #104 | semidirect |
| 200. #1502 | D59 | semidirect |
| 232. C59 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434671 | 2 |
| #21425016 | 2 |
| #21425014 | 2 |
| C4×#14273658 | 2 |
| #21422592 | 2 |
| #21422386 | 2 |
| C59×#1502 | 2 |
| #9721 | 59 |