Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #21437230 | C2 | semidirect |
| 2. C2×#16837838 | C2 | semidirect |
| 3. #21425832 | C2 | semidirect |
| 4. #21425812 | C2 | semidirect |
| 5. #21424994 | C2 | semidirect |
| 6. #21422182 | C2 | semidirect |
| 7. C59×#3155 | C2 | semidirect |
| 38. C2×Dic236 | D4 | semidirect |
| 40. C2×D472 | D4 | semidirect |
| 51. #14273667 | D4 | semidirect |
| 53. C2×C59⋊C16 | D4 | semidirect |
| 213. #3155 | D59 | semidirect |
| 250. C59 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| C2×#16837838 | 2 |
| #21425832 | 2 |
| #21425812 | 2 |
| #21424994 | 2 |
| #21422182 | 2 |
| C59×#3155 | 2 |
| #13334 | 59 |