Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×#15690555 | C2 | semidirect |
| 2. #20259925 | C2 | direct (N × H) |
| 3. C2×#15690543 | C2 | semidirect |
| 4. C2×#15690540 | C2 | semidirect |
| 5. C2×#15690539 | C2 | semidirect |
| 6. C22×D4×C193 | C2 | semidirect |
| 8. #15690555 | C22 | semidirect |
| 9. C2×Dic386 | C22 | semidirect |
| 10. C2×D772 | C22 | semidirect |
| 13. #15690543 | C22 | semidirect |
| 14. #15690540 | C22 | semidirect |
| 15. #15690539 | C22 | semidirect |
| 16. C2×#13095393 | C22 | semidirect |
| 21. C2×D4×C193 | C22 | semidirect |
| 25. Dic386 | C23 | semidirect |
| 27. D772 | C23 | semidirect |
| 31. #13095393 | C23 | semidirect |
| 57. C2×C193 | AGL(1,ℤ/8) | semidirect |
| 60. C193 | C2×AGL(1,ℤ/8) | semidirect |
| 63. C22×D4 | D193 | semidirect |
| 77. C2×D4 | C2×D193 | semidirect |
| 119. C2 | #20259925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690555 | 2 |
| #20259925 | 2 |
| C2×#15690543 | 2 |
| C2×#15690540 | 2 |
| C2×#15690539 | 2 |
| C22×D4×C193 | 2 |
| C2×AGL(1,ℤ/8) | 193 |