Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
494 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 494 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. #21425781 | C2 | semidirect |
| 3. #21422245 | C2 | semidirect |
| 4. C59×#1525 | C2 | semidirect |
| 15. #16837199 | C22 | semidirect |
| 19. C59×#329 | C22 | semidirect |
| 170. #1525 | D59 | semidirect |
| 192. #329 | C2×D59 | semidirect |
| 193. C59 | #13564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433444 | 2 |
| #21425781 | 2 |
| #21422245 | 2 |
| C59×#1525 | 2 |
| #13564 | 59 |