Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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×#16838759 | C2 | semidirect |
| 2. C2×C8×D241 | C2 | semidirect |
| 3. #21440622 | C2 | semidirect |
| 5. #21440565 | C2 | semidirect |
| 6. #21440562 | C2 | semidirect |
| 7. #106×C241 | C2 | semidirect |
| 36. C8×C241 | D4 | semidirect |
| 43. C2×D241 | SD16 | semidirect |
| 55. C241 | #465 | semidirect |
| 61. #106 | D241 | semidirect |
| 92. C8 | D964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838759 | 2 |
| C2×C8×D241 | 2 |
| #21440622 | 2 |
| #21440617 | 2 |
| #21440565 | 2 |
| #21440562 | 2 |
| #106×C241 | 2 |
| #465 | 241 |