Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 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. #21432981 | C2 | semidirect |
| 3. #21425833 | C2 | semidirect |
| 4. C2×#16837213 | C2 | semidirect |
| 5. #21424994 | C2 | semidirect |
| 6. #21422202 | C2 | semidirect |
| 7. C59×#1378 | C2 | semidirect |
| 12. #16837845 | C4 | semidirect |
| 14. #16837840 | C4 | semidirect |
| 39. C2×Dic236 | C2×C4 | semidirect |
| 43. C2×D472 | C2×C4 | semidirect |
| 70. M32×C59 | C2×C4 | semidirect |
| 190. #1378 | D59 | semidirect |
| 218. C59 | #13030 | semidirect |
| 252. M32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437232 | 2 |
| #21432981 | 2 |
| #21425833 | 2 |
| C2×#16837213 | 2 |
| #21424994 | 2 |
| #21422202 | 2 |
| C59×#1378 | 2 |
| #13030 | 59 |