Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21425897 | C2 | semidirect |
| 3. #21422856 | C2 | semidirect |
| 4. #21422064 | C2 | semidirect |
| 5. #21422063 | C2 | semidirect |
| 6. #21422062 | C2 | semidirect |
| 7. C59×#1333 | C2 | semidirect |
| 21. #16837178 | C22 | semidirect |
| 23. #16837153 | C22 | semidirect |
| 25. C59×#346 | C22 | semidirect |
| 26. C59×#334 | C22 | semidirect |
| 166. #1333 | D59 | semidirect |
| 188. #346 | C2×D59 | semidirect |
| 191. #334 | C2×D59 | semidirect |
| 192. C59 | #11667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D59 | 2 |
| #21425897 | 2 |
| #21422856 | 2 |
| #21422064 | 2 |
| #21422063 | 2 |
| #21422062 | 2 |
| C59×#1333 | 2 |
| #11667 | 59 |