Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21435294 | C2 | semidirect |
| 3. #21424927 | C2 | semidirect |
| 4. #21422608 | C2 | semidirect |
| 5. #21422604 | C2 | semidirect |
| 6. #21422007 | C2 | semidirect |
| 7. C59×#3254 | C2 | semidirect |
| 197. #3254 | D59 | semidirect |
| 235. C59 | #10214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435294 | 2 |
| #21435091 | 2 |
| #21424927 | 2 |
| #21422608 | 2 |
| #21422604 | 2 |
| #21422007 | 2 |
| C59×#3254 | 2 |
| #10214 | 59 |