Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #21429973 | C2 | semidirect |
| 5. #21422542 | C2 | semidirect |
| 6. #21421962 | C2 | semidirect |
| 7. C59×#1534 | C2 | semidirect |
| 188. #1534 | D59 | semidirect |
| 222. C59 | #10021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434499 | 2 |
| #21434219 | 2 |
| #21429973 | 2 |
| #21422644 | 2 |
| #21422542 | 2 |
| #21421962 | 2 |
| C59×#1534 | 2 |
| #10021 | 59 |