Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×C4×Dic193 | C2 | semidirect |
| 3. #20259825 | C2 | direct (N × H) |
| 4. C2×M16×C193 | C2 | semidirect |
| 7. #15690555 | C4 | semidirect |
| 9. C2×Dic386 | C4 | semidirect |
| 10. C2×D772 | C4 | semidirect |
| 15. C4×Dic193 | C22 | semidirect |
| 18. M16×C193 | C22 | semidirect |
| 22. Dic386 | C2×C4 | semidirect |
| 24. D772 | C2×C4 | semidirect |
| 54. C2×C193 | #104 | semidirect |
| 57. C193 | C2×#104 | semidirect |
| 60. C2×M16 | D193 | semidirect |
| 74. M16 | C2×D193 | semidirect |
| 113. C2 | #20259825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690555 | 2 |
| C2×C4×Dic193 | 2 |
| #20259825 | 2 |
| C2×M16×C193 | 2 |
| C2×#104 | 193 |