Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21433083 | C2 | semidirect |
| 3. #21422538 | C2 | semidirect |
| 4. #21422436 | C2 | semidirect |
| 5. C59⋊#1308 | C2 | semidirect |
| 6. #21421967 | C2 | semidirect |
| 7. C59×#1535 | C2 | semidirect |
| 201. #1535 | D59 | semidirect |
| 239. C59 | #9532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434230 | 2 |
| #21433083 | 2 |
| #21422538 | 2 |
| #21422436 | 2 |
| C59⋊#1308 | 2 |
| #21421967 | 2 |
| C59×#1535 | 2 |
| #9532 | 59 |