Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21425850 | C2 | semidirect |
| 3. #21422858 | C2 | semidirect |
| 4. #21422152 | C2 | semidirect |
| 5. #21422150 | C2 | semidirect |
| 6. #21422142 | C2 | semidirect |
| 7. C59×#1361 | C2 | semidirect |
| 139. #1361 | D59 | semidirect |
| 162. C59 | #11985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434673 | 2 |
| #21425850 | 2 |
| #21422858 | 2 |
| #21422152 | 2 |
| #21422150 | 2 |
| #21422142 | 2 |
| C59×#1361 | 2 |
| #11985 | 59 |