Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
636 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16837718 | C2 | semidirect |
| 3. #21428588 | C2 | semidirect |
| 4. #21424184 | C2 | semidirect |
| 5. #21422663 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 7. C59×#1964 | C2 | semidirect |
| 216. #1964 | D59 | semidirect |
| 252. C59 | #9950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434844 | 2 |
| C2×#16837718 | 2 |
| #21428588 | 2 |
| #21424184 | 2 |
| #21422663 | 2 |
| #21421944 | 2 |
| C59×#1964 | 2 |
| #9950 | 59 |