Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21426015 | C2 | semidirect |
| 3. #21426012 | C2 | semidirect |
| 4. #21425420 | C2 | semidirect |
| 5. #21422104 | C2 | semidirect |
| 6. #21422035 | C2 | semidirect |
| 7. C59×#1347 | C2 | semidirect |
| 139. C2×Dic59 | SD32 | semidirect |
| 177. #1347 | D59 | semidirect |
| 205. C59 | #12161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435402 | 2 |
| #21426015 | 2 |
| #21426012 | 2 |
| #21425420 | 2 |
| #21422104 | 2 |
| #21422035 | 2 |
| C59×#1347 | 2 |
| #12161 | 59 |