Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
792 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 792 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. #21429826 | C2 | semidirect |
| 3. #21424933 | C2 | semidirect |
| 4. #21424039 | C2 | semidirect |
| 5. #21422616 | C2 | semidirect |
| 6. #21422001 | C2 | semidirect |
| 7. C59×#3193 | C2 | semidirect |
| 260. #3193 | D59 | semidirect |
| 301. C59 | #9931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433346 | 2 |
| #21429826 | 2 |
| #21424933 | 2 |
| #21424039 | 2 |
| #21422616 | 2 |
| #21422001 | 2 |
| C59×#3193 | 2 |
| #9931 | 59 |