Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21423463 | C2 | semidirect |
| 4. #21422154 | C2 | semidirect |
| 5. #21422076 | C2 | semidirect |
| 7. C59×#2241 | C2 | semidirect |
| 123. #2241 | D59 | semidirect |
| 150. C59 | #12359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436965 | 2 |
| #21426138 | 2 |
| #21423463 | 2 |
| #21422154 | 2 |
| #21422076 | 2 |
| #21422058 | 2 |
| C59×#2241 | 2 |
| #12359 | 59 |