Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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×#10620297 | C2 | semidirect |
| 2. D41⋊M16 | C2 | direct (N × H) |
| 3. C2×#10620301 | C2 | semidirect |
| 4. C2×#10620296 | C2 | semidirect |
| 15. #10620301 | C22 | semidirect |
| 16. C2×#66493 | C22 | semidirect |
| 17. #10620297 | C22 | semidirect |
| 18. #10620296 | C22 | semidirect |
| 37. #66493 | C23 | semidirect |
| 43. C2×D41 | M16 | semidirect |
| 52. C2×C41 | C2×M16 | semidirect |
| 55. D41 | C2×M16 | semidirect |
| 57. C41 | C22×M16 | semidirect |
| 111. C2 | D41⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620297 | 2 |
| D41⋊M16 | 2 |
| C2×#10620301 | 2 |
| C2×#10620296 | 2 |
| C22×C4×D41 | 2 |
| C22×M16 | 41 |