Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #21425076 | C2 | semidirect |
| 5. #21422659 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1286 | C2 | semidirect |
| 11. #16837775 | C4 | semidirect |
| 12. #16837749 | C4 | semidirect |
| 32. #14273727 | C2×C4 | semidirect |
| 33. #14273727 | C2×C4 | semidirect |
| 64. C4×C8×C59 | C2×C4 | semidirect |
| 115. C4×Dic59 | SD16 | semidirect |
| 194. #1286 | D59 | semidirect |
| 221. C59 | #9295 | semidirect |
| 257. C4×C8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435039 | 2 |
| #21426819 | 2 |
| #21425076 | 2 |
| #21422765 | 2 |
| #21422659 | 2 |
| #21421924 | 2 |
| C59×#1286 | 2 |
| #9295 | 59 |