Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 3. #21424146 | C2 | semidirect |
| 4. #21422224 | C2 | semidirect |
| 5. C59×#1812 | C2 | semidirect |
| 6. C22×C8×D59 | C4 | semidirect |
| 13. #16837430 | C4 | semidirect |
| 16. #16837365 | C4 | semidirect |
| 17. #16837357 | C4 | semidirect |
| 184. #1812 | D59 | semidirect |
| 211. C59 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432788 | 2 |
| #21425735 | 2 |
| #21424146 | 2 |
| #21422224 | 2 |
| C59×#1812 | 2 |
| #12805 | 59 |