Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×D1928 | C2 | semidirect |
| 2. C2×#16838755 | C2 | semidirect |
| 3. #21440638 | C2 | semidirect |
| 4. #21440604 | C2 | semidirect |
| 5. #21440571 | C2 | semidirect |
| 6. #21440562 | C2 | semidirect |
| 7. #102×C241 | C2 | semidirect |
| 26. D964 | D4 | semidirect |
| 53. Dic241 | D8 | semidirect |
| 60. C241 | #459 | semidirect |
| 68. #102 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1928 | 2 |
| C2×#16838755 | 2 |
| #21440638 | 2 |
| #21440604 | 2 |
| #21440571 | 2 |
| #21440562 | 2 |
| #102×C241 | 2 |
| #459 | 241 |