Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21425705 | C2 | semidirect |
| 3. #21424124 | C2 | semidirect |
| 4. #21422109 | C2 | semidirect |
| 5. #21422107 | C2 | semidirect |
| 6. #21422105 | C2 | semidirect |
| 7. C59×#1347 | C2 | semidirect |
| 8. C2×#14273746 | C4 | semidirect |
| 12. #16837644 | C4 | semidirect |
| 14. #16837635 | C4 | semidirect |
| 17. #16837439 | C4 | semidirect |
| 189. #1347 | D59 | semidirect |
| 217. C59 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433675 | 2 |
| #21425705 | 2 |
| #21424124 | 2 |
| #21422109 | 2 |
| #21422107 | 2 |
| #21422105 | 2 |
| C59×#1347 | 2 |
| #11890 | 59 |