Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
772 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 772 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. #21433144 | C2 | semidirect |
| 3. #21424026 | C2 | semidirect |
| 4. #21424016 | C2 | semidirect |
| 5. #21422002 | C2 | semidirect |
| 6. #21421972 | C2 | semidirect |
| 7. C59×#1513 | C2 | semidirect |
| 11. #16837552 | C4 | semidirect |
| 13. #16837535 | C4 | semidirect |
| 270. #1513 | D59 | semidirect |
| 307. C59 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433322 | 2 |
| #21433144 | 2 |
| #21424026 | 2 |
| #21424016 | 2 |
| #21422002 | 2 |
| #21421972 | 2 |
| C59×#1513 | 2 |
| #9520 | 59 |