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. #21425831 | C2 | semidirect |
| 3. #21425811 | C2 | semidirect |
| 4. #21425717 | C2 | semidirect |
| 5. C59×#1812 | C2 | semidirect |
| 11. C2×#14273749 | C4 | semidirect |
| 13. C22×D472 | C4 | semidirect |
| 15. C2×#14273667 | C22 | semidirect |
| 20. C59×#427 | C22 | semidirect |
| 173. #1812 | D59 | semidirect |
| 191. #427 | 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 |
| #21425831 | 2 |
| #21425811 | 2 |
| #21425717 | 2 |
| C59×#1812 | 2 |
| #12741 | 59 |