Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
458 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21423944 | C2 | semidirect |
| 3. #21423843 | C2 | semidirect |
| 4. #21421922 | C2 | semidirect |
| 7. C59×#1272 | C2 | semidirect |
| 193. #1272 | D59 | semidirect |
| 223. C59 | #7676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432470 | 2 |
| #21423944 | 2 |
| #21423843 | 2 |
| #21421922 | 2 |
| #21421916 | 2 |
| C59×#1272 | 2 |
| #7676 | 59 |