Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
620 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 620 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. #21427272 | C2 | semidirect |
| 3. #21422809 | C2 | semidirect |
| 4. #21422643 | C2 | semidirect |
| 5. #21421962 | C2 | semidirect |
| 6. #21421960 | C2 | semidirect |
| 7. C59×#1514 | C2 | semidirect |
| 11. #16837778 | C4 | semidirect |
| 12. #16837776 | C4 | semidirect |
| 45. C4×C59⋊C8 | C2×C4 | semidirect |
| 50. C4⋊Q8×C59 | C2×C4 | semidirect |
| 51. #127×C59 | C2×C4 | semidirect |
| 180. #1514 | D59 | semidirect |
| 206. C59 | #9428 | semidirect |
| 217. C4⋊Q8 | C4×D59 | semidirect |
| 222. #127 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434549 | 2 |
| #21427272 | 2 |
| #21422809 | 2 |
| #21422643 | 2 |
| #21421962 | 2 |
| #21421960 | 2 |
| C59×#1514 | 2 |
| #9428 | 59 |