Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
486 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 486 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. #21422758 | C2 | semidirect |
| 3. #21422240 | C2 | semidirect |
| 4. C59×#2126 | C2 | semidirect |
| 5. #16838238 | C4 | semidirect |
| 8. #16837579 | C4 | semidirect |
| 13. #16837386 | C4 | semidirect |
| 15. #16837146 | C22 | semidirect |
| 19. C59×#353 | C22 | semidirect |
| 169. #2126 | D59 | semidirect |
| 190. #353 | C2×D59 | semidirect |
| 193. C59 | #13560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433444 | 2 |
| #21422758 | 2 |
| #21422240 | 2 |
| C59×#2126 | 2 |
| #13560 | 59 |