Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 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 |
|---|---|---|
| 3. #20259830 | C2 | semidirect |
| 4. #20259823 | C2 | semidirect |
| 6. C4×#13095393 | C2 | semidirect |
| 7. C4×Q8×C193 | C2 | semidirect |
| 10. #15690542 | C4 | direct (N × H) |
| 26. #13095393 | C2×C4 | semidirect |
| 28. Q8×C193 | C2×C4 | semidirect |
| 41. C4×C193 | SD16 | semidirect |
| 49. C193 | C4×SD16 | semidirect |
| 52. C4×Q8 | D193 | semidirect |
| 72. Q8 | C4×D193 | semidirect |
| 92. C4 | #15690542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690542 | 2 |
| C4×D772 | 2 |
| #20259830 | 2 |
| #20259823 | 2 |
| #20259819 | 2 |
| C4×#13095393 | 2 |
| C4×Q8×C193 | 2 |
| C4×SD16 | 193 |