Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #21424216 | C2 | semidirect |
| 3. #21422792 | C2 | semidirect |
| 4. #21422791 | C2 | semidirect |
| 5. #21422603 | C2 | semidirect |
| 6. #21421965 | C2 | semidirect |
| 7. C59×#1505 | C2 | semidirect |
| 164. #1505 | D59 | semidirect |
| 191. C59 | #10513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435403 | 2 |
| #21424216 | 2 |
| #21422792 | 2 |
| #21422791 | 2 |
| #21422603 | 2 |
| #21421965 | 2 |
| C59×#1505 | 2 |
| #10513 | 59 |