Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
610 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21434037 | C2 | semidirect |
| 3. #21429886 | C2 | semidirect |
| 4. #21424932 | C2 | semidirect |
| 5. #21424196 | C2 | semidirect |
| 6. #21422003 | C2 | semidirect |
| 7. C59×#1507 | C2 | semidirect |
| 232. #1507 | D59 | semidirect |
| 268. C59 | #9932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434893 | 2 |
| #21434037 | 2 |
| #21429886 | 2 |
| #21424932 | 2 |
| #21424196 | 2 |
| #21422003 | 2 |
| C59×#1507 | 2 |
| #9932 | 59 |