Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D241 | C2 | semidirect |
| 3. #21440641 | C2 | semidirect |
| 4. #21440628 | C2 | semidirect |
| 5. #21440627 | C2 | semidirect |
| 6. #21440624 | C2 | semidirect |
| 7. #21440622 | C2 | semidirect |
| 8. #21440621 | C2 | semidirect |
| 9. #21440618 | C2 | semidirect |
| 10. #21440600 | C2 | semidirect |
| 11. C22⋊Q8×C241 | C2 | semidirect |
| 83. C241 | #536 | semidirect |
| 94. C22⋊Q8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838770 | 2 |
| C2×Q8×D241 | 2 |
| #21440641 | 2 |
| #21440628 | 2 |
| #21440627 | 2 |
| #21440624 | 2 |
| #21440622 | 2 |
| #21440621 | 2 |
| #21440618 | 2 |
| #21440600 | 2 |
| C22⋊Q8×C241 | 2 |
| #536 | 241 |