Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
624 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21433165 | C2 | semidirect |
| 3. #21425779 | C2 | semidirect |
| 4. #21424047 | C2 | semidirect |
| 5. #21422219 | C2 | semidirect |
| 6. #21422218 | C2 | semidirect |
| 7. C59×#1791 | C2 | semidirect |
| 258. #1791 | D59 | semidirect |
| 293. C59 | #13052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433445 | 2 |
| #21433165 | 2 |
| #21425779 | 2 |
| #21424047 | 2 |
| #21422219 | 2 |
| #21422218 | 2 |
| C59×#1791 | 2 |
| #13052 | 59 |