Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
354 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 354 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. #21425897 | C2 | semidirect |
| 3. #334×D59 | C2 | semidirect |
| 4. #21422064 | C2 | semidirect |
| 5. #21422063 | C2 | semidirect |
| 6. #21422062 | C2 | semidirect |
| 7. C59×#1333 | C2 | semidirect |
| 160. #1333 | D59 | semidirect |
| 186. C59 | #11654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434672 | 2 |
| #21425897 | 2 |
| #334×D59 | 2 |
| #21422064 | 2 |
| #21422063 | 2 |
| #21422062 | 2 |
| C59×#1333 | 2 |
| #11654 | 59 |