Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 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. #349×D59 | C2 | semidirect |
| 3. #21422034 | C2 | semidirect |
| 4. #21422033 | C2 | semidirect |
| 5. C59×#1321 | C2 | semidirect |
| 15. #16837184 | C22 | semidirect |
| 18. C59×#349 | C22 | semidirect |
| 174. #1321 | D59 | semidirect |
| 194. #349 | C2×D59 | semidirect |
| 195. C59 | #11438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432538 | 2 |
| #349×D59 | 2 |
| #21422034 | 2 |
| #21422033 | 2 |
| C59×#1321 | 2 |
| #11438 | 59 |