Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 2. C2×#16837225 | C2 | semidirect |
| 5. #21424824 | C2 | semidirect |
| 6. #21422195 | C2 | semidirect |
| 7. C59×#1376 | C2 | semidirect |
| 19. #16837213 | C4 | semidirect |
| 92. Dic236 | C4⋊C4 | semidirect |
| 94. D472 | C4⋊C4 | semidirect |
| 157. #1376 | D59 | semidirect |
| 180. C59 | #12950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837520 | 2 |
| C2×#16837225 | 2 |
| C2×#16837213 | 2 |
| #21424824 | 2 |
| #21422195 | 2 |
| C59×#1376 | 2 |
| #12950 | 59 |