Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #21424220 | C2 | semidirect |
| 5. #21422202 | C2 | semidirect |
| 6. #21422195 | C2 | semidirect |
| 7. C59×#2153 | C2 | semidirect |
| 10. #16837515 | C4 | semidirect |
| 11. #16837510 | C4 | semidirect |
| 147. #2153 | D59 | semidirect |
| 175. C59 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432981 | 2 |
| #21425833 | 2 |
| #21425825 | 2 |
| #21424220 | 2 |
| #21422202 | 2 |
| #21422195 | 2 |
| C59×#2153 | 2 |
| #12828 | 59 |