Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
566 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21426975 | C2 | semidirect |
| 4. #21424187 | C2 | semidirect |
| 5. #21421963 | C2 | semidirect |
| 6. #21421942 | C2 | semidirect |
| 12. C2×#14273658 | C4 | semidirect |
| 13. C2×#14273648 | C4 | semidirect |
| 252. C59 | #9261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837718 | 2 |
| #21426975 | 2 |
| #21424933 | 2 |
| #21424187 | 2 |
| #21421963 | 2 |
| #21421942 | 2 |
| C59×#1519 | 2 |
| #9261 | 59 |