Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
502 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21433166 | C2 | semidirect |
| 3. #21422756 | C2 | semidirect |
| 4. #21422565 | C2 | semidirect |
| 5. #21421996 | C2 | semidirect |
| 6. #21421994 | C2 | semidirect |
| 7. C59×#1496 | C2 | semidirect |
| 167. #1496 | D59 | semidirect |
| 195. C59 | #9007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434541 | 2 |
| #21433166 | 2 |
| #21422756 | 2 |
| #21422565 | 2 |
| #21421996 | 2 |
| #21421994 | 2 |
| C59×#1496 | 2 |
| #9007 | 59 |