Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1162 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 147 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×#16837216 | C2 | semidirect |
| 3. #21424134 | C2 | semidirect |
| 4. C59×#2112 | C2 | semidirect |
| 11. C2×#14273663 | C22 | semidirect |
| 16. C2×M32×C59 | C22 | semidirect |
| 112. C22×C59 | #361 | semidirect |
| 125. #2112 | D59 | semidirect |
| 139. C2×M32 | C2×D59 | semidirect |
| 145. C59 | #12736 | semidirect |
| 243. C22 | #16837216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D472 | 2 |
| C2×#16837216 | 2 |
| #21424134 | 2 |
| C59×#2112 | 2 |
| #12736 | 59 |