Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #21424837 | C2 | semidirect |
| 5. #21422201 | C2 | semidirect |
| 6. #21422179 | C2 | semidirect |
| 7. C59×#2159 | C2 | semidirect |
| 19. #16837213 | C4 | semidirect |
| 52. #14273659 | C2×C4 | semidirect |
| 64. M32×C59 | C2×C4 | semidirect |
| 113. Dic236 | C4⋊C4 | semidirect |
| 115. D472 | C4⋊C4 | semidirect |
| 177. #2159 | D59 | semidirect |
| 209. C59 | #12943 | semidirect |
| 236. M32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432896 | 2 |
| C2×#16837213 | 2 |
| #21425806 | 2 |
| #21424837 | 2 |
| #21422201 | 2 |
| #21422179 | 2 |
| C59×#2159 | 2 |
| #12943 | 59 |