Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
428 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21425885 | C2 | semidirect |
| 3. C2×#16837214 | C2 | semidirect |
| 4. C2×#16837204 | C2 | semidirect |
| 5. C2×#16837185 | C2 | semidirect |
| 6. #21424157 | C2 | semidirect |
| 7. C59×#1382 | C2 | semidirect |
| 49. #14273667 | D4 | semidirect |
| 183. #1382 | D59 | semidirect |
| 210. C59 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433745 | 2 |
| #21425885 | 2 |
| C2×#16837214 | 2 |
| C2×#16837204 | 2 |
| C2×#16837185 | 2 |
| #21424157 | 2 |
| C59×#1382 | 2 |
| #13387 | 59 |