Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 61 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. #21426174 | C2 | semidirect |
| 3. #21423703 | C2 | semidirect |
| 4. #21422132 | C2 | semidirect |
| 5. #21422069 | C2 | semidirect |
| 6. #21422068 | C2 | semidirect |
| 7. C59×#2214 | C2 | semidirect |
| 17. #16837223 | C22 | semidirect |
| 19. C8×C59⋊C8 | C22 | semidirect |
| 21. C59×#494 | C22 | semidirect |
| 23. C59×#364 | C22 | semidirect |
| 142. #2214 | D59 | semidirect |
| 156. #494 | C2×D59 | semidirect |
| 165. #364 | C2×D59 | semidirect |
| 169. C59 | #12312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435896 | 2 |
| #21426174 | 2 |
| #21423703 | 2 |
| #21422132 | 2 |
| #21422069 | 2 |
| #21422068 | 2 |
| C59×#2214 | 2 |
| #12312 | 59 |