Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
348 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21422393 | C2 | semidirect |
| 3. #21422071 | C2 | semidirect |
| 4. #21422068 | C2 | semidirect |
| 5. C59×#2165 | C2 | semidirect |
| 16. #16837123 | C22 | semidirect |
| 17. C8×C59⋊C8 | C22 | semidirect |
| 19. C59×#364 | C22 | semidirect |
| 121. #2165 | D59 | semidirect |
| 139. #364 | C2×D59 | semidirect |
| 145. C59 | #11670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433007 | 2 |
| #21422393 | 2 |
| #21422071 | 2 |
| #21422068 | 2 |
| C59×#2165 | 2 |
| #11670 | 59 |