Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
504 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #21422781 | C2 | semidirect |
| 5. #21421987 | C2 | semidirect |
| 6. #21421985 | C2 | semidirect |
| 7. C59×#1549 | C2 | semidirect |
| 173. #1549 | D59 | semidirect |
| 203. C59 | #9435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434553 | 2 |
| #21433162 | 2 |
| #21422829 | 2 |
| #21422781 | 2 |
| #21421987 | 2 |
| #21421985 | 2 |
| C59×#1549 | 2 |
| #9435 | 59 |