Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #21432731 | C2 | semidirect |
| 3. #21424944 | C2 | semidirect |
| 4. #21424934 | C2 | semidirect |
| 5. #21424024 | C2 | semidirect |
| 6. #21424016 | C2 | semidirect |
| 7. C59×#1785 | C2 | semidirect |
| 16. #16837425 | C22 | semidirect |
| 17. C2×#14273646 | C22 | semidirect |
| 18. C2×#14273644 | C22 | semidirect |
| 22. M16×Dic59 | C22 | semidirect |
| 24. C2×#101×C59 | C22 | semidirect |
| 25. C2×#100×C59 | C22 | semidirect |
| 180. #1785 | D59 | semidirect |
| 200. C2×#101 | C2×D59 | semidirect |
| 204. C2×#100 | C2×D59 | semidirect |
| 208. C59 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837966 | 2 |
| #21432731 | 2 |
| #21424944 | 2 |
| #21424934 | 2 |
| #21424024 | 2 |
| #21424016 | 2 |
| C59×#1785 | 2 |
| #21801 | 59 |