Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
734 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 734 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 |
|---|---|---|
| 1. #21434097 | C2 | semidirect |
| 2. #21434096 | C2 | semidirect |
| 3. #21427375 | C2 | semidirect |
| 4. #21424927 | C2 | semidirect |
| 5. #21422520 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1486 | C2 | semidirect |
| 39. #14273727 | D4 | semidirect |
| 40. #14273724 | D4 | semidirect |
| 67. C4×C59⋊C8 | D4 | semidirect |
| 84. C4×C8×C59 | D4 | semidirect |
| 142. C4×Dic59 | D8 | semidirect |
| 234. #1486 | D59 | semidirect |
| 268. C59 | #10012 | semidirect |
| 318. C4×C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434097 | 2 |
| #21434096 | 2 |
| #21427375 | 2 |
| #21424927 | 2 |
| #21422520 | 2 |
| #21421924 | 2 |
| C59×#1486 | 2 |
| #10012 | 59 |