Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
468 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 468 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. #21425767 | C2 | semidirect |
| 3. #21425747 | C2 | semidirect |
| 4. #21424142 | C2 | semidirect |
| 5. C59×#1757 | C2 | semidirect |
| 6. C22×D472 | C4 | semidirect |
| 13. #16837440 | C4 | semidirect |
| 14. #16837408 | C4 | semidirect |
| 166. #1757 | D59 | semidirect |
| 191. C59 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433744 | 2 |
| #21425767 | 2 |
| #21425747 | 2 |
| #21424142 | 2 |
| C59×#1757 | 2 |
| #13231 | 59 |