Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #21424269 | C2 | semidirect |
| 5. #21422194 | C2 | semidirect |
| 6. #21422179 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 136. #1383 | D59 | semidirect |
| 156. C59 | #13487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837216 | 2 |
| C2×#16837214 | 2 |
| #21424970 | 2 |
| #21424269 | 2 |
| #21422194 | 2 |
| #21422179 | 2 |
| C59×#1383 | 2 |
| #13487 | 59 |