Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21426413 | C2 | semidirect |
| 2. C2×#16837240 | C2 | semidirect |
| 3. #21426221 | C2 | semidirect |
| 4. #21422286 | C2 | semidirect |
| 5. #21422280 | C2 | semidirect |
| 6. #21422238 | C2 | semidirect |
| 8. C2×Dic472 | C22 | semidirect |
| 13. #16837236 | C22 | semidirect |
| 14. C2×C59⋊C32 | C22 | semidirect |
| 15. #16837232 | C22 | semidirect |
| 144. C59 | #13671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426413 | 2 |
| C2×#16837240 | 2 |
| #21426221 | 2 |
| #21422286 | 2 |
| #21422280 | 2 |
| #21422238 | 2 |
| C59×#3415 | 2 |
| #13671 | 59 |