Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #21440636 | C2 | semidirect |
| 2. #21440634 | C2 | semidirect |
| 3. #21440630 | C2 | semidirect |
| 4. #21440625 | C2 | semidirect |
| 5. #21440621 | C2 | semidirect |
| 7. C4×Dic482 | C2 | semidirect |
| 8. C4×D964 | C2 | semidirect |
| 9. C4×C22⋊D241 | C2 | semidirect |
| 10. #21440599 | C2 | semidirect |
| 11. C2×C42×C241 | C2 | semidirect |
| 74. C241 | #529 | semidirect |
| 86. C2×C42 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440636 | 2 |
| #21440634 | 2 |
| #21440630 | 2 |
| #21440625 | 2 |
| #21440621 | 2 |
| #21440616 | 2 |
| C4×Dic482 | 2 |
| C4×D964 | 2 |
| C4×C22⋊D241 | 2 |
| #21440599 | 2 |
| C2×C42×C241 | 2 |
| #529 | 241 |