Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21425882 | C2 | semidirect |
| 3. C2×#16837211 | C2 | semidirect |
| 4. #21425806 | C2 | semidirect |
| 5. C2×#16837184 | C2 | semidirect |
| 6. #21422203 | C2 | semidirect |
| 7. C59×#1809 | C2 | semidirect |
| 49. #14273667 | D4 | semidirect |
| 206. #1809 | D59 | semidirect |
| 236. C59 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433705 | 2 |
| #21425882 | 2 |
| C2×#16837211 | 2 |
| #21425806 | 2 |
| C2×#16837184 | 2 |
| #21422203 | 2 |
| C59×#1809 | 2 |
| #13386 | 59 |