Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16837138 | C2 | semidirect |
| 4. #21422461 | C2 | semidirect |
| 5. #21421983 | C2 | semidirect |
| 6. #21421939 | C2 | semidirect |
| 10. #16837730 | C4 | semidirect |
| 11. #16837713 | C4 | semidirect |
| 15. #16837557 | C4 | semidirect |
| 16. #16837540 | C4 | semidirect |
| 268. C59 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434873 | 2 |
| #21433152 | 2 |
| C2×#16837138 | 2 |
| #21422461 | 2 |
| #21421983 | 2 |
| #21421939 | 2 |
| C59×#1504 | 2 |
| #9263 | 59 |