Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 536 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. #21424132 | C2 | semidirect |
| 3. #21423874 | C2 | semidirect |
| 4. #21422611 | C2 | semidirect |
| 5. #21422457 | C2 | semidirect |
| 6. #21422456 | C2 | semidirect |
| 7. C59×#1507 | C2 | semidirect |
| 8. C22×#11745669 | C4 | semidirect |
| 16. C2×#14273660 | C4 | semidirect |
| 17. C2×#14273648 | C4 | semidirect |
| 18. C2×#14273647 | C4 | semidirect |
| 221. #1507 | D59 | semidirect |
| 255. C59 | #9818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837636 | 2 |
| #21424132 | 2 |
| #21423874 | 2 |
| #21422611 | 2 |
| #21422457 | 2 |
| #21422456 | 2 |
| C59×#1507 | 2 |
| #9818 | 59 |