Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
374 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21422866 | C2 | semidirect |
| 5. #21421992 | C2 | semidirect |
| 6. #21421991 | C2 | semidirect |
| 7. C59×#1571 | C2 | semidirect |
| 158. #1571 | D59 | semidirect |
| 186. C59 | #8863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432733 | 2 |
| #21424077 | 2 |
| #21422866 | 2 |
| #21422408 | 2 |
| #21421992 | 2 |
| #21421991 | 2 |
| C59×#1571 | 2 |
| #8863 | 59 |