Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
212 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21425934 | C2 | semidirect |
| 3. #21422171 | C2 | semidirect |
| 4. #21422069 | C2 | semidirect |
| 5. #21422068 | C2 | semidirect |
| 6. #21422012 | C2 | semidirect |
| 7. C59×#2170 | C2 | semidirect |
| 25. #14273673 | C8 | semidirect |
| 26. #14273671 | C8 | semidirect |
| 27. #14273670 | C8 | semidirect |
| 28. #14273668 | C8 | semidirect |
| 101. #2170 | D59 | semidirect |
| 125. C59 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425975 | 2 |
| #21425934 | 2 |
| #21422171 | 2 |
| #21422069 | 2 |
| #21422068 | 2 |
| #21422012 | 2 |
| C59×#2170 | 2 |
| #12047 | 59 |