Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
494 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 494 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. #21422661 | C2 | semidirect |
| 4. #21422594 | C2 | semidirect |
| 6. #21421956 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 11. #16837693 | C4 | semidirect |
| 12. #16837683 | C4 | semidirect |
| 190. #1303 | D59 | semidirect |
| 219. C59 | #9177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433895 | 2 |
| #21427067 | 2 |
| #21422661 | 2 |
| #21422594 | 2 |
| #21422488 | 2 |
| #21421956 | 2 |
| C59×#1303 | 2 |
| #9177 | 59 |