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. C22×D772 | C2 | semidirect |
| 3. #20259927 | C2 | direct (N × H) |
| 4. C2×#15690544 | C2 | semidirect |
| 5. C2×D1544 | C2 | semidirect |
| 6. C2×M16×C193 | C2 | semidirect |
| 9. #15690555 | C22 | semidirect |
| 10. C2×Dic386 | C22 | semidirect |
| 14. C2×D772 | C22 | semidirect |
| 15. C2×D772 | C22 | semidirect |
| 18. #15690544 | C22 | semidirect |
| 19. D1544 | C22 | semidirect |
| 21. M16×C193 | C22 | semidirect |
| 22. C2×C8×C193 | C22 | semidirect |
| 28. Dic386 | C23 | semidirect |
| 33. D772 | C23 | semidirect |
| 42. C8×C193 | C23 | semidirect |
| 56. C2×C193 | AGL(1,ℤ/8) | semidirect |
| 60. C193 | C2×AGL(1,ℤ/8) | semidirect |
| 67. C2×M16 | D193 | semidirect |
| 82. M16 | C2×D193 | semidirect |
| 83. C2×C8 | C2×D193 | semidirect |
| 103. C8 | C22×D193 | semidirect |
| 119. C2 | #20259927 | 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 |
| C22×D772 | 2 |
| #20259927 | 2 |
| C2×#15690544 | 2 |
| C2×D1544 | 2 |
| C2×M16×C193 | 2 |
| C2×AGL(1,ℤ/8) | 193 |