Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21425761 | C2 | semidirect |
| 3. #21422254 | C2 | semidirect |
| 4. C59×#2132 | C2 | semidirect |
| 7. C2×#14273724 | C4 | semidirect |
| 8. #16837792 | C4 | semidirect |
| 13. C4×#11745664 | C4 | semidirect |
| 14. #16837197 | C22 | semidirect |
| 19. C59×#355 | C22 | semidirect |
| 152. #2132 | D59 | semidirect |
| 173. #355 | C2×D59 | semidirect |
| 176. C59 | #13579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434549 | 2 |
| #21425761 | 2 |
| #21422254 | 2 |
| C59×#2132 | 2 |
| #13579 | 59 |