Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
572 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21423948 | C2 | semidirect |
| 3. #21423840 | C2 | semidirect |
| 4. #21421917 | C2 | semidirect |
| 5. #21421916 | C2 | semidirect |
| 6. #21421916 | C2 | semidirect |
| 7. C59×#1270 | C2 | semidirect |
| 224. #1270 | D59 | semidirect |
| 253. C59 | #7679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432450 | 2 |
| #21423948 | 2 |
| #21423840 | 2 |
| #21421917 | 2 |
| #21421916 | 2 |
| C59×#1270 | 2 |
| #7679 | 59 |