Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
302 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21426281 | C2 | semidirect |
| 3. #21426276 | C2 | semidirect |
| 4. #21422110 | C2 | semidirect |
| 5. #21422110 | C2 | semidirect |
| 6. #21422038 | C2 | semidirect |
| 7. C59×#2089 | C2 | semidirect |
| 146. #2089 | D59 | semidirect |
| 175. C59 | #12294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435535 | 2 |
| #21426281 | 2 |
| #21426276 | 2 |
| #21422110 | 2 |
| #21422038 | 2 |
| C59×#2089 | 2 |
| #12294 | 59 |