Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21433110 | C2 | semidirect |
| 3. #21422695 | C2 | semidirect |
| 4. #21422447 | C2 | semidirect |
| 5. #21422006 | C2 | semidirect |
| 6. #21421987 | C2 | semidirect |
| 7. C59×#1488 | C2 | semidirect |
| 205. #1488 | D59 | semidirect |
| 240. C59 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433590 | 2 |
| #21433110 | 2 |
| #21422695 | 2 |
| #21422447 | 2 |
| #21422006 | 2 |
| #21421987 | 2 |
| C59×#1488 | 2 |
| #9349 | 59 |