Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21425911 | C2 | semidirect |
| 3. #21425860 | C2 | semidirect |
| 4. #21422158 | C2 | semidirect |
| 5. #21422156 | C2 | semidirect |
| 6. #21422137 | C2 | semidirect |
| 7. C59×#1359 | C2 | semidirect |
| 142. #1359 | D59 | semidirect |
| 166. C59 | #11991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434721 | 2 |
| #21425911 | 2 |
| #21425860 | 2 |
| #21422158 | 2 |
| #21422156 | 2 |
| #21422137 | 2 |
| C59×#1359 | 2 |
| #11991 | 59 |