Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 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. #21432754 | C2 | semidirect |
| 5. #21421972 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 7. C59×#1826 | C2 | semidirect |
| 16. C2×#14273660 | C4 | semidirect |
| 17. C2×#14273658 | C4 | semidirect |
| 19. C2×#14273647 | C4 | semidirect |
| 20. C2×#14273647 | C4 | semidirect |
| 218. #1826 | D59 | semidirect |
| 256. C59 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837726 | 2 |
| #21432754 | 2 |
| #21422611 | 2 |
| #21422457 | 2 |
| #21421972 | 2 |
| #21421944 | 2 |
| C59×#1826 | 2 |
| #9242 | 59 |