Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
444 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16837226 | C2 | semidirect |
| 3. C2×#16837214 | C2 | semidirect |
| 4. C2×#16837212 | C2 | semidirect |
| 5. C2×#16837180 | C2 | semidirect |
| 6. #21424972 | C2 | semidirect |
| 7. C59×#1975 | C2 | semidirect |
| 11. C2×#14273670 | C4 | semidirect |
| 12. C2×#14273668 | C4 | semidirect |
| 111. C59⋊C16 | C22⋊C4 | semidirect |
| 172. #1975 | D59 | semidirect |
| 199. C59 | #13249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837837 | 2 |
| C2×#16837226 | 2 |
| C2×#16837214 | 2 |
| C2×#16837212 | 2 |
| C2×#16837180 | 2 |
| #21424972 | 2 |
| C59×#1975 | 2 |
| #13249 | 59 |