Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D241 | C2 | semidirect |
| 2. C2×#16838759 | C2 | semidirect |
| 3. C2×#16838757 | C2 | semidirect |
| 5. #21440565 | C2 | semidirect |
| 6. #21440554 | C2 | semidirect |
| 7. #103×C241 | C2 | semidirect |
| 27. Dic482 | D4 | semidirect |
| 38. Q8×C241 | D4 | semidirect |
| 49. C2×D241 | SD16 | semidirect |
| 61. C241 | #448 | semidirect |
| 68. #103 | D241 | semidirect |
| 91. Q8 | D964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D241 | 2 |
| C2×#16838759 | 2 |
| C2×#16838757 | 2 |
| #21440617 | 2 |
| #21440565 | 2 |
| #21440554 | 2 |
| #103×C241 | 2 |
| #448 | 241 |