Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. #21433122 | C2 | semidirect |
| 3. #21424081 | C2 | semidirect |
| 4. #21424027 | C2 | semidirect |
| 5. #21421964 | C2 | semidirect |
| 6. #21421963 | C2 | semidirect |
| 7. C59×#1786 | C2 | semidirect |
| 18. #16837316 | C4 | semidirect |
| 19. #16837310 | C4 | semidirect |
| 33. C22×C59⋊C8 | D4 | semidirect |
| 70. C22×C8×C59 | D4 | semidirect |
| 273. #1786 | D59 | semidirect |
| 308. C59 | #9472 | semidirect |
| 323. C22×C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433122 | 2 |
| #21427446 | 2 |
| #21424081 | 2 |
| #21424027 | 2 |
| #21421964 | 2 |
| #21421963 | 2 |
| C59×#1786 | 2 |
| #9472 | 59 |