Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21440637 | C2 | semidirect |
| 2. #21440633 | C2 | semidirect |
| 3. #21440627 | C2 | semidirect |
| 4. #21440626 | C2 | semidirect |
| 5. #21440618 | C2 | semidirect |
| 7. #21440602 | C2 | semidirect |
| 8. C2×#16838749 | C2 | semidirect |
| 9. C22⋊Q8×C241 | C2 | semidirect |
| 66. C241 | #539 | semidirect |
| 73. C22⋊Q8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440637 | 2 |
| #21440633 | 2 |
| #21440627 | 2 |
| #21440626 | 2 |
| #21440618 | 2 |
| #21440616 | 2 |
| #21440602 | 2 |
| C2×#16838749 | 2 |
| C22⋊Q8×C241 | 2 |
| #539 | 241 |