Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
124 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 55 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×#16838753 | C2 | semidirect |
| 3. #21440571 | C2 | semidirect |
| 4. C22⋊#14515349 | C2 | semidirect |
| 5. #21440554 | C2 | semidirect |
| 6. #21440552 | C2 | semidirect |
| 7. C22×C8×C241 | C2 | semidirect |
| 36. C8×C241 | D4 | semidirect |
| 39. C22×C241 | M16 | semidirect |
| 55. C241 | #435 | semidirect |
| 58. C22×C8 | D241 | semidirect |
| 92. C8 | C22⋊D241 | semidirect |
| 98. C22 | #16838753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838753 | 2 |
| C4×C22⋊D241 | 2 |
| #21440571 | 2 |
| C22⋊#14515349 | 2 |
| #21440554 | 2 |
| #21440552 | 2 |
| C22×C8×C241 | 2 |
| #435 | 241 |