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. #21424942 | C2 | semidirect |
| 4. #21424934 | C2 | semidirect |
| 5. #21424022 | C2 | semidirect |
| 6. #21424017 | C2 | semidirect |
| 7. C59×#1783 | C2 | semidirect |
| 16. #16837425 | C22 | semidirect |
| 17. C2×#14273645 | C22 | semidirect |
| 19. C2×#14273643 | C22 | semidirect |
| 21. M16×Dic59 | C22 | semidirect |
| 159. #1783 | D59 | semidirect |
| 183. C59 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837969 | 2 |
| #21432731 | 2 |
| #21424942 | 2 |
| #21424934 | 2 |
| #21424022 | 2 |
| #21424017 | 2 |
| C59×#1783 | 2 |
| #21801 | 59 |