Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C2×#16838760 | C2 | semidirect |
| 4. #21440575 | C2 | semidirect |
| 5. #21440566 | C2 | semidirect |
| 6. #21440565 | C2 | semidirect |
| 38. C22×C241 | Q16 | semidirect |
| 51. C241 | #467 | semidirect |
| 90. C22 | #16838760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838760 | 2 |
| C22×#14515349 | 2 |
| #21440621 | 2 |
| #21440575 | 2 |
| #21440566 | 2 |
| #21440565 | 2 |
| C22⋊Q8×C241 | 2 |
| #467 | 241 |