Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1170 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 147 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. #21423858 | C2 | semidirect |
| 3. C2×#16837141 | C2 | semidirect |
| 4. C59×#1749 | C2 | semidirect |
| 15. C2×#14273638 | C22 | semidirect |
| 20. C2×#97×C59 | C22 | semidirect |
| 180. C22×C59 | #329 | semidirect |
| 205. #1749 | D59 | semidirect |
| 229. C2×#97 | C2×D59 | semidirect |
| 233. C59 | #8334 | semidirect |
| 399. C22 | #16837141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273715 | 2 |
| #21423858 | 2 |
| C2×#16837141 | 2 |
| C59×#1749 | 2 |
| #8334 | 59 |