Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
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×#20238620 | C2 | semidirect |
| 2. D373⋊M16 | C2 | direct (N × H) |
| 3. C2×#20238619 | C2 | semidirect |
| 4. C2×D373⋊C8 | C2 | semidirect |
| 6. #20238620 | C22 | semidirect |
| 7. #20238619 | C22 | semidirect |
| 8. D373⋊C8 | C22 | semidirect |
| 9. C2×#15688419 | C22 | semidirect |
| 19. #15688419 | C23 | semidirect |
| 43. C2×D373 | M16 | semidirect |
| 52. C2×C373 | C2×M16 | semidirect |
| 55. D373 | C2×M16 | semidirect |
| 56. C373 | C22×M16 | semidirect |
| 111. C2 | D373⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238620 | 2 |
| D373⋊M16 | 2 |
| C2×#20238619 | 2 |
| C2×D373⋊C8 | 2 |
| C22×C4×D373 | 2 |
| C22×M16 | 373 |