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. #21426909 | C2 | semidirect |
| 3. #21422693 | C2 | semidirect |
| 4. #21422643 | C2 | semidirect |
| 5. #21421961 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#1980 | C2 | semidirect |
| 9. #16837789 | C4 | semidirect |
| 10. #16837764 | C4 | semidirect |
| 54. #14273638 | C2×C4 | semidirect |
| 63. C4⋊Q8×C59 | C2×C4 | semidirect |
| 64. #127×C59 | C2×C4 | semidirect |
| 217. #1980 | 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 |
| #21426909 | 2 |
| #21422693 | 2 |
| #21422643 | 2 |
| #21421961 | 2 |
| #21421952 | 2 |
| C59×#1980 | 2 |
| #9381 | 59 |