Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21434492 | C2 | semidirect |
| 3. #21425086 | C2 | semidirect |
| 4. #21422688 | C2 | semidirect |
| 5. #21422512 | C2 | semidirect |
| 6. #21421987 | C2 | semidirect |
| 7. C59×#3226 | C2 | semidirect |
| 180. #3226 | D59 | semidirect |
| 215. C59 | #10110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435474 | 2 |
| #21434492 | 2 |
| #21425086 | 2 |
| #21422688 | 2 |
| #21422512 | 2 |
| #21421987 | 2 |
| C59×#3226 | 2 |
| #10110 | 59 |