Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #21434643 | C2 | semidirect |
| 4. #21424940 | C2 | semidirect |
| 6. #21421987 | C2 | semidirect |
| 7. C59×#1485 | C2 | semidirect |
| 180. #1485 | D59 | semidirect |
| 210. C59 | #10116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435479 | 2 |
| #21435226 | 2 |
| #21434643 | 2 |
| #21424940 | 2 |
| #21422687 | 2 |
| #21421987 | 2 |
| C59×#1485 | 2 |
| #10116 | 59 |