Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21424381 | C2 | semidirect |
| 5. #21424318 | C2 | semidirect |
| 6. #21422226 | C2 | semidirect |
| 7. C59×#1392 | C2 | semidirect |
| 190. #1392 | D59 | semidirect |
| 218. C59 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433154 | 2 |
| #21425738 | 2 |
| #21424512 | 2 |
| #21424381 | 2 |
| #21424318 | 2 |
| #21422226 | 2 |
| C59×#1392 | 2 |
| #12963 | 59 |