Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
930 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21425833 | C2 | semidirect |
| 3. #21425813 | C2 | semidirect |
| 4. #21424142 | C2 | semidirect |
| 5. C59×#2115 | C2 | semidirect |
| 11. C2×#14273749 | C4 | semidirect |
| 13. C22×D472 | C4 | semidirect |
| 15. #16837440 | C22 | semidirect |
| 21. C2×M32×C59 | C22 | semidirect |
| 172. #2115 | D59 | semidirect |
| 190. C2×M32 | C2×D59 | semidirect |
| 197. C59 | #12741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838207 | 2 |
| #21425833 | 2 |
| #21425813 | 2 |
| #21424142 | 2 |
| C59×#2115 | 2 |
| #12741 | 59 |