Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21424089 | C2 | semidirect |
| 3. #21422855 | C2 | semidirect |
| 5. C2×#16837134 | C2 | semidirect |
| 6. #21421970 | C2 | semidirect |
| 217. C59 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433564 | 2 |
| #21424089 | 2 |
| #21422855 | 2 |
| #21422773 | 2 |
| C2×#16837134 | 2 |
| #21421970 | 2 |
| C59×#1492 | 2 |
| #10458 | 59 |