Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21424224 | C2 | semidirect |
| 3. #21422109 | C2 | semidirect |
| 5. C59×#2163 | C2 | semidirect |
| 7. #16837804 | C4 | semidirect |
| 8. #16837786 | C4 | semidirect |
| 13. C4×Dic236 | C4 | semidirect |
| 15. C4×D472 | C4 | semidirect |
| 143. #2163 | D59 | semidirect |
| 170. C59 | #11860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434666 | 2 |
| #21424224 | 2 |
| #21422109 | 2 |
| #21422106 | 2 |
| C59×#2163 | 2 |
| #11860 | 59 |