Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21425882 | C2 | semidirect |
| 4. #21424879 | C2 | semidirect |
| 5. #21422192 | C2 | semidirect |
| 6. #21422184 | C2 | semidirect |
| 20. #16837215 | C4 | semidirect |
| 36. #14273667 | C2×C4 | semidirect |
| 39. #14273663 | C2×C4 | semidirect |
| 185. C59 | #12940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432948 | 2 |
| #21425882 | 2 |
| C2×#16837215 | 2 |
| #21424879 | 2 |
| #21422192 | 2 |
| #21422184 | 2 |
| C2×C59×#357 | 2 |
| #12940 | 59 |