Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #21434127 | C2 | semidirect |
| 3. #21424928 | C2 | semidirect |
| 4. #21422525 | C2 | semidirect |
| 5. #21422521 | C2 | semidirect |
| 6. #21421925 | C2 | semidirect |
| 7. C59×#2398 | C2 | semidirect |
| 213. #2398 | D59 | semidirect |
| 249. C59 | #10013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434127 | 2 |
| #21434096 | 2 |
| #21424928 | 2 |
| #21422525 | 2 |
| #21422521 | 2 |
| #21421925 | 2 |
| C59×#2398 | 2 |
| #10013 | 59 |