Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1140 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 1. #21432378 | C2 | semidirect |
| 2. #21425519 | C2 | semidirect |
| 3. #21425279 | C2 | semidirect |
| 4. #21425094 | C2 | semidirect |
| 5. C59×#1779 | C2 | semidirect |
| 6. C22×D472 | C22 | semidirect |
| 9. C2×#14273661 | C22 | semidirect |
| 10. C2×#14273649 | C22 | semidirect |
| 13. #16837165 | C22 | semidirect |
| 14. #16837165 | C22 | semidirect |
| 41. C24×C59 | D8 | semidirect |
| 117. #1779 | D59 | semidirect |
| 135. C59 | #32706 | semidirect |
| 160. C24 | D472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432378 | 2 |
| #21425519 | 2 |
| #21425279 | 2 |
| #21425094 | 2 |
| C59×#1779 | 2 |
| #32706 | 59 |