Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
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×#17989812 | C2 | semidirect |
| 2. D293⋊M16 | C2 | direct (N × H) |
| 3. C2×#17989811 | C2 | semidirect |
| 4. C2×D293⋊C8 | C2 | semidirect |
| 6. #17989812 | C22 | semidirect |
| 7. #17989811 | C22 | semidirect |
| 8. D293⋊C8 | C22 | semidirect |
| 9. C2×#14556880 | C22 | semidirect |
| 19. #14556880 | C23 | semidirect |
| 43. C2×D293 | M16 | semidirect |
| 52. C2×C293 | C2×M16 | semidirect |
| 55. D293 | C2×M16 | semidirect |
| 56. C293 | C22×M16 | semidirect |
| 111. C2 | D293⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989812 | 2 |
| D293⋊M16 | 2 |
| C2×#17989811 | 2 |
| C2×D293⋊C8 | 2 |
| C22×C4×D293 | 2 |
| C22×M16 | 293 |