Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
594 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21424932 | C2 | semidirect |
| 3. #21424119 | C2 | semidirect |
| 4. #21423874 | C2 | semidirect |
| 5. #21422664 | C2 | semidirect |
| 6. #21422663 | C2 | semidirect |
| 7. C59×#1964 | C2 | semidirect |
| 8. C22×#11745669 | C4 | semidirect |
| 15. C2×#14273660 | C4 | semidirect |
| 17. C2×#14273648 | C4 | semidirect |
| 18. C2×#14273647 | C4 | semidirect |
| 202. C59⋊C8 | #99 | semidirect |
| 237. #1964 | D59 | semidirect |
| 274. C59 | #9785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837636 | 2 |
| #21424932 | 2 |
| #21424119 | 2 |
| #21423874 | 2 |
| #21422664 | 2 |
| #21422663 | 2 |
| C59×#1964 | 2 |
| #9785 | 59 |