Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21440690 | C2 | semidirect |
| 2. #21440689 | C2 | semidirect |
| 3. #21440675 | C2 | semidirect |
| 4. #21440674 | C2 | semidirect |
| 5. #21440671 | C2 | semidirect |
| 6. #21440663 | C2 | semidirect |
| 7. #21440662 | C2 | semidirect |
| 8. C2×#16838760 | C2 | semidirect |
| 9. Q16×D241 | C2 | semidirect |
| 10. #21440650 | C2 | semidirect |
| 11. #137×C241 | C2 | semidirect |
| 87. C241 | #578 | semidirect |
| 94. #137 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440690 | 2 |
| #21440689 | 2 |
| #21440675 | 2 |
| #21440674 | 2 |
| #21440671 | 2 |
| #21440663 | 2 |
| #21440662 | 2 |
| C2×#16838760 | 2 |
| Q16×D241 | 2 |
| #21440650 | 2 |
| #137×C241 | 2 |
| #578 | 241 |