Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 51 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. #20259830 | C2 | semidirect |
| 4. #20259820 | C2 | semidirect |
| 5. #20259819 | C2 | semidirect |
| 6. #20259810 | C2 | semidirect |
| 7. C4×D4×C193 | C2 | semidirect |
| 10. #15690540 | C4 | semidirect |
| 22. D772 | C2×C4 | semidirect |
| 26. #13095393 | C2×C4 | semidirect |
| 29. D4×C193 | C2×C4 | semidirect |
| 53. C193 | #442 | semidirect |
| 57. C4×D4 | D193 | semidirect |
| 79. D4 | C4×D193 | semidirect |
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 |
| #20259830 | 2 |
| #20259820 | 2 |
| #20259819 | 2 |
| #20259810 | 2 |
| C4×D4×C193 | 2 |
| #442 | 193 |