Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20259894 | C2 | semidirect |
| 2. #20259890 | C2 | semidirect |
| 3. #20259888 | C2 | semidirect |
| 4. #20259884 | C2 | semidirect |
| 5. #20259875 | C2 | semidirect |
| 7. C4×D772 | C2 | semidirect |
| 8. C4×D772 | C2 | semidirect |
| 9. #20259856 | C2 | semidirect |
| 10. C42×D193 | C2 | semidirect |
| 11. C4×Q8×C193 | C2 | semidirect |
| 74. C193 | #529 | semidirect |
| 82. C4×Q8 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259894 | 2 |
| #20259890 | 2 |
| #20259888 | 2 |
| #20259884 | 2 |
| #20259875 | 2 |
| #20259874 | 2 |
| C4×D772 | 2 |
| #20259856 | 2 |
| C42×D193 | 2 |
| C4×Q8×C193 | 2 |
| #529 | 193 |