Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21426906 | C2 | semidirect |
| 3. #21425016 | C2 | semidirect |
| 4. #21422695 | C2 | semidirect |
| 5. #21421960 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1514 | C2 | semidirect |
| 9. #16837789 | C4 | semidirect |
| 10. #16837764 | C4 | semidirect |
| 58. #14273638 | C2×C4 | semidirect |
| 64. C4⋊Q8×C59 | C2×C4 | semidirect |
| 65. #127×C59 | C2×C4 | semidirect |
| 219. #1514 | D59 | semidirect |
| 252. C59 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D59 | semidirect |
| 261. #127 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435079 | 2 |
| #21426906 | 2 |
| #21425016 | 2 |
| #21422695 | 2 |
| #21421960 | 2 |
| #21421953 | 2 |
| C59×#1514 | 2 |
| #9381 | 59 |