Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. #21438496 | C2 | semidirect |
| 2. #21435087 | C2 | semidirect |
| 3. #21423417 | C2 | semidirect |
| 4. #21423388 | C2 | semidirect |
| 5. #21422734 | C2 | semidirect |
| 6. #21422706 | C2 | semidirect |
| 7. C59×#3135 | C2 | semidirect |
| 160. #3135 | D59 | semidirect |
| 192. C59 | #19061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438496 | 2 |
| #21435087 | 2 |
| #21423417 | 2 |
| #21423388 | 2 |
| #21422734 | 2 |
| #21422706 | 2 |
| C59×#3135 | 2 |
| #19061 | 59 |