Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
466 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. C2×#16837834 | C2 | semidirect |
| 2. #21426416 | C2 | semidirect |
| 3. #21426411 | C2 | semidirect |
| 4. #21426405 | C2 | semidirect |
| 5. C2×C59×M64 | C2 | semidirect |
| 10. #16837834 | C22 | semidirect |
| 11. C2×Dic472 | C22 | semidirect |
| 13. C2×D944 | C22 | semidirect |
| 14. Dic944 | C22 | semidirect |
| 15. #16837241 | C22 | semidirect |
| 16. D1888 | C22 | semidirect |
| 18. C59×M64 | C22 | semidirect |
| 19. C2×C32×C59 | C22 | semidirect |
| 94. C2×M64 | D59 | semidirect |
| 111. M64 | C2×D59 | semidirect |
| 112. C2×C32 | C2×D59 | semidirect |
| 113. C59 | #33981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837834 | 2 |
| #21426416 | 2 |
| #21426411 | 2 |
| #21426405 | 2 |
| C2×C59×M64 | 2 |
| #33981 | 59 |