Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 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×D772 | C2 | semidirect |
| 3. #20259832 | C2 | semidirect |
| 4. #20259820 | C2 | semidirect |
| 5. #20259819 | C2 | semidirect |
| 6. C4×#13095393 | C2 | semidirect |
| 7. C4×D4×C193 | C2 | semidirect |
| 10. #15690540 | C4 | direct (N × H) |
| 22. D772 | C2×C4 | semidirect |
| 26. #13095393 | C2×C4 | semidirect |
| 29. D4×C193 | C2×C4 | semidirect |
| 44. C4×C193 | D8 | semidirect |
| 53. C193 | C4×D8 | semidirect |
| 57. C4×D4 | D193 | semidirect |
| 79. D4 | C4×D193 | semidirect |
| 99. C4 | #15690540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690540 | 2 |
| C4×D772 | 2 |
| #20259832 | 2 |
| #20259820 | 2 |
| #20259819 | 2 |
| C4×#13095393 | 2 |
| C4×D4×C193 | 2 |
| C4×D8 | 193 |