Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 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. #135×Dic59 | C2 | semidirect |
| 3. #21425833 | C2 | semidirect |
| 4. #21424982 | C2 | semidirect |
| 5. #21422210 | C2 | semidirect |
| 6. #21422177 | C2 | semidirect |
| 7. C59×#2143 | C2 | semidirect |
| 11. #16837842 | C4 | semidirect |
| 13. #16837837 | C4 | semidirect |
| 34. C2×Dic236 | C2×C4 | semidirect |
| 36. C2×D472 | C2×C4 | semidirect |
| 50. #14273667 | C2×C4 | semidirect |
| 189. #2143 | D59 | semidirect |
| 220. C59 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| #135×Dic59 | 2 |
| #21425833 | 2 |
| #21424982 | 2 |
| #21422210 | 2 |
| #21422177 | 2 |
| C59×#2143 | 2 |
| #13027 | 59 |