Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 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. #21433225 | C2 | semidirect |
| 3. #21424924 | C2 | semidirect |
| 4. C4×#14273655 | C2 | semidirect |
| 5. #21422512 | C2 | semidirect |
| 6. #21421987 | C2 | semidirect |
| 7. C59×#1276 | C2 | semidirect |
| 11. #16837698 | C4 | semidirect |
| 12. #16837693 | C4 | semidirect |
| 13. #16837603 | C4 | semidirect |
| 14. #16837598 | C4 | semidirect |
| 179. Dic118 | #104 | semidirect |
| 217. #1276 | D59 | semidirect |
| 249. C59 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434157 | 2 |
| #21433225 | 2 |
| #21424924 | 2 |
| C4×#14273655 | 2 |
| #21422512 | 2 |
| #21421987 | 2 |
| C59×#1276 | 2 |
| #8970 | 59 |