Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21425717 | C2 | semidirect |
| 3. #21422080 | C2 | semidirect |
| 4. C59×#1812 | C2 | semidirect |
| 5. C22×D472 | C4 | semidirect |
| 8. #16837655 | C4 | semidirect |
| 12. #16837440 | C4 | semidirect |
| 15. #16837184 | C22 | semidirect |
| 19. C59×H(3,ℤ/4) | C22 | semidirect |
| 147. #1812 | D59 | semidirect |
| 169. H(3,ℤ/4) | C2×D59 | semidirect |
| 170. C59 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433744 | 2 |
| #21425717 | 2 |
| #21422080 | 2 |
| C59×#1812 | 2 |
| #11868 | 59 |