Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #21435413 | C2 | semidirect |
| 2. #21434196 | C2 | semidirect |
| 4. #21424893 | C2 | semidirect |
| 5. #21422712 | C2 | semidirect |
| 6. #21422708 | C2 | semidirect |
| 7. C59×#1290 | C2 | semidirect |
| 207. #1290 | D59 | semidirect |
| 239. C59 | #10027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435413 | 2 |
| #21434196 | 2 |
| #21434188 | 2 |
| #21424893 | 2 |
| #21422712 | 2 |
| #21422708 | 2 |
| C59×#1290 | 2 |
| #10027 | 59 |