Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
518 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21434649 | C2 | semidirect |
| 3. #21422722 | C2 | semidirect |
| 4. #21422647 | C2 | semidirect |
| 6. #21421962 | C2 | semidirect |
| 227. C59 | #10023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434649 | 2 |
| #21429964 | 2 |
| #21422722 | 2 |
| #21422647 | 2 |
| #21422539 | 2 |
| #21421962 | 2 |
| C59×#3110 | 2 |
| #10023 | 59 |