Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21425040 | C2 | semidirect |
| 4. #21422607 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1300 | C2 | semidirect |
| 11. #16837683 | C4 | semidirect |
| 12. #16837608 | C4 | semidirect |
| 181. #1300 | D59 | semidirect |
| 210. C59 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434196 | 2 |
| #21426740 | 2 |
| #21425040 | 2 |
| #21422607 | 2 |
| #21422540 | 2 |
| #21421953 | 2 |
| C59×#1300 | 2 |
| #9327 | 59 |