Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
426 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21424211 | C2 | semidirect |
| 3. #21423843 | C2 | semidirect |
| 4. #21421920 | C2 | semidirect |
| 5. #21421918 | C2 | semidirect |
| 220. C59 | #7706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432460 | 2 |
| #21424211 | 2 |
| #21423843 | 2 |
| #21421920 | 2 |
| #21421918 | 2 |
| #21421917 | 2 |
| C59×#1270 | 2 |
| #7706 | 59 |