Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20259893 | C2 | semidirect |
| 2. #20259891 | C2 | semidirect |
| 3. #20259887 | C2 | semidirect |
| 4. #20259882 | C2 | semidirect |
| 5. #20259878 | C2 | semidirect |
| 7. C4×Dic386 | C2 | semidirect |
| 8. C4×D772 | C2 | semidirect |
| 9. C4×C22⋊D193 | C2 | semidirect |
| 10. #20259856 | C2 | semidirect |
| 11. C2×C42×C193 | C2 | semidirect |
| 74. C193 | #529 | semidirect |
| 86. C2×C42 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259893 | 2 |
| #20259891 | 2 |
| #20259887 | 2 |
| #20259882 | 2 |
| #20259878 | 2 |
| #20259873 | 2 |
| C4×Dic386 | 2 |
| C4×D772 | 2 |
| C4×C22⋊D193 | 2 |
| #20259856 | 2 |
| C2×C42×C193 | 2 |
| #529 | 193 |