Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21433150 | C2 | semidirect |
| 3. #21422601 | C2 | semidirect |
| 4. C2×#16837136 | C2 | semidirect |
| 5. #21421983 | C2 | semidirect |
| 6. #21421938 | C2 | semidirect |
| 7. C59×#1471 | C2 | semidirect |
| 9. #16837737 | C4 | semidirect |
| 11. #16837720 | C4 | semidirect |
| 14. #16837553 | C4 | semidirect |
| 16. #16837536 | C4 | semidirect |
| 240. #1471 | D59 | semidirect |
| 280. C59 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434861 | 2 |
| #21433150 | 2 |
| #21422601 | 2 |
| C2×#16837136 | 2 |
| #21421983 | 2 |
| #21421938 | 2 |
| C59×#1471 | 2 |
| #9264 | 59 |