Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21425939 | C2 | semidirect |
| 3. #21422163 | C2 | semidirect |
| 4. #21422072 | C2 | semidirect |
| 5. #21422071 | C2 | semidirect |
| 6. #21422018 | C2 | semidirect |
| 7. C59×#2171 | C2 | semidirect |
| 25. #14273673 | C8 | semidirect |
| 26. #14273671 | C8 | semidirect |
| 27. #14273670 | C8 | semidirect |
| 28. #14273668 | C8 | semidirect |
| 100. #2171 | D59 | semidirect |
| 124. C59 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425980 | 2 |
| #21425939 | 2 |
| #21422163 | 2 |
| #21422072 | 2 |
| #21422071 | 2 |
| #21422018 | 2 |
| C59×#2171 | 2 |
| #12068 | 59 |