Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 408 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. #21424832 | C2 | semidirect |
| 5. #21422206 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 7. C2×C59×#365 | C2 | semidirect |
| 18. #16837207 | C4 | semidirect |
| 19. #16837204 | C4 | semidirect |
| 92. Dic236 | C4⋊C4 | semidirect |
| 94. D472 | C4⋊C4 | semidirect |
| 151. C2×#365 | D59 | semidirect |
| 180. C59 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837523 | 2 |
| C2×#16837211 | 2 |
| #21425809 | 2 |
| #21424832 | 2 |
| #21422206 | 2 |
| #21422175 | 2 |
| C2×C59×#365 | 2 |
| #12955 | 59 |