Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 2. C4×Dic386 | C2 | semidirect |
| 3. C4×D772 | C2 | semidirect |
| 4. C4×C22⋊D193 | C2 | semidirect |
| 5. #20259858 | C2 | semidirect |
| 6. #20259856 | C2 | semidirect |
| 7. C42×D193 | C2 | semidirect |
| 8. C2×C42×C193 | C2 | semidirect |
| 9. #15690555 | C4 | direct (N × H) |
| 27. Dic386 | C2×C4 | semidirect |
| 28. D772 | C2×C4 | semidirect |
| 29. C22⋊D193 | C2×C4 | semidirect |
| 33. C4×D193 | C2×C4 | semidirect |
| 36. C2×C4×C193 | C2×C4 | semidirect |
| 49. C4×C193 | #41 | semidirect |
| 56. C193 | C4×#41 | semidirect |
| 65. C2×C42 | D193 | semidirect |
| 93. C2×C4 | C4×D193 | semidirect |
| 108. C4 | #15690555 | 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 |
| C4×Dic386 | 2 |
| C4×D772 | 2 |
| C4×C22⋊D193 | 2 |
| #20259858 | 2 |
| #20259856 | 2 |
| C42×D193 | 2 |
| C2×C42×C193 | 2 |
| C4×#41 | 193 |