Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 3. #21424144 | C2 | semidirect |
| 4. #21424140 | C2 | semidirect |
| 5. #21422226 | C2 | semidirect |
| 6. #21422224 | C2 | semidirect |
| 9. C23×C59⋊C8 | C4 | semidirect |
| 16. #16837429 | C4 | semidirect |
| 20. #16837366 | C4 | semidirect |
| 21. #16837358 | C4 | semidirect |
| 238. C59 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432791 | 2 |
| #21425737 | 2 |
| #21424144 | 2 |
| #21424140 | 2 |
| #21422226 | 2 |
| #21422224 | 2 |
| C59×#2120 | 2 |
| #12805 | 59 |