Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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. C4×#14273662 | C2 | semidirect |
| 3. #21422857 | C2 | semidirect |
| 6. #21421967 | C2 | semidirect |
| 7. C59×#1291 | C2 | semidirect |
| 168. #1291 | D59 | semidirect |
| 197. C59 | #8693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433065 | 2 |
| C4×#14273662 | 2 |
| #21422857 | 2 |
| #21422704 | 2 |
| #21422701 | 2 |
| #21421967 | 2 |
| C59×#1291 | 2 |
| #8693 | 59 |