Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×Dic482 | C2 | semidirect |
| 4. #21440576 | C2 | semidirect |
| 5. #21440567 | C2 | semidirect |
| 7. #97×C241 | C2 | semidirect |
| 11. #16838759 | C4 | semidirect |
| 22. Dic482 | C2×C4 | semidirect |
| 33. C8×C241 | C2×C4 | semidirect |
| 49. C241 | #440 | semidirect |
| 57. #97 | D241 | semidirect |
| 83. C8 | C4×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838759 | 2 |
| C4×Dic482 | 2 |
| C4×D964 | 2 |
| #21440576 | 2 |
| #21440567 | 2 |
| #21440564 | 2 |
| #97×C241 | 2 |
| #440 | 241 |