Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21425983 | C2 | semidirect |
| 3. #21425973 | C2 | semidirect |
| 4. #21422302 | C2 | semidirect |
| 5. #21422287 | C2 | semidirect |
| 6. #21422284 | C2 | semidirect |
| 7. C59×#1398 | C2 | semidirect |
| 12. #16837241 | C4 | semidirect |
| 13. D1888 | C4 | semidirect |
| 25. Dic472 | C2×C4 | semidirect |
| 29. D944 | C2×C4 | semidirect |
| 38. C32×C59 | C2×C4 | semidirect |
| 90. #1398 | D59 | semidirect |
| 108. C59 | #13658 | semidirect |
| 126. C32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426411 | 2 |
| #21425983 | 2 |
| #21425973 | 2 |
| #21422302 | 2 |
| #21422287 | 2 |
| #21422284 | 2 |
| C59×#1398 | 2 |
| #13658 | 59 |