Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 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. #21440637 | C2 | semidirect |
| 2. #21440633 | C2 | semidirect |
| 3. #21440632 | C2 | semidirect |
| 5. #21440622 | C2 | semidirect |
| 6. #21440621 | C2 | semidirect |
| 7. #21440607 | C2 | semidirect |
| 9. #21440601 | C2 | semidirect |
| 10. #21440600 | C2 | semidirect |
| 11. C2×C4⋊C4×C241 | C2 | semidirect |
| 72. C241 | #552 | semidirect |
| 84. C2×C4⋊C4 | 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 |
| #21440632 | 2 |
| #21440625 | 2 |
| #21440622 | 2 |
| #21440621 | 2 |
| #21440607 | 2 |
| C4×C22⋊D241 | 2 |
| #21440601 | 2 |
| #21440600 | 2 |
| C2×C4⋊C4×C241 | 2 |
| #552 | 241 |