Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21424088 | C2 | semidirect |
| 3. #21422871 | C2 | semidirect |
| 4. #21422763 | C2 | semidirect |
| 5. #21422763 | C2 | semidirect |
| 6. #21421992 | C2 | semidirect |
| 7. C59×#1478 | C2 | semidirect |
| 182. #1478 | 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 |
| #21424088 | 2 |
| #21422871 | 2 |
| #21422763 | 2 |
| #21421992 | 2 |
| C59×#1478 | 2 |
| #10440 | 59 |