Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21422872 | C2 | semidirect |
| 3. #21422765 | C2 | semidirect |
| 4. #21422765 | C2 | semidirect |
| 5. #21422487 | C2 | semidirect |
| 6. #21421991 | C2 | semidirect |
| 7. C59×#1800 | C2 | semidirect |
| 178. #1800 | D59 | semidirect |
| 208. C59 | #10440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837597 | 2 |
| #21422872 | 2 |
| #21422765 | 2 |
| #21422487 | 2 |
| #21421991 | 2 |
| C59×#1800 | 2 |
| #10440 | 59 |