Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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×C22⋊D193 | C2 | semidirect |
| 3. #20259859 | C2 | semidirect |
| 4. #20259855 | C2 | semidirect |
| 5. C2×C22⋊Dic193 | C2 | semidirect |
| 6. C22⋊C4×D193 | C2 | semidirect |
| 7. C2×C22⋊C4×C193 | C2 | semidirect |
| 9. C2×C22⋊D193 | C4 | semidirect |
| 13. C22×Dic193 | C22 | semidirect |
| 14. C2×C4×D193 | C22 | semidirect |
| 15. #15690534 | C22 | semidirect |
| 17. C22⋊Dic193 | C22 | semidirect |
| 18. #15690532 | C22 | semidirect |
| 19. C4×Dic193 | C22 | semidirect |
| 21. C22×C4×C193 | C22 | semidirect |
| 23. C22⋊C4×C193 | C22 | semidirect |
| 25. C22×D193 | C2×C4 | semidirect |
| 27. C22⋊D193 | C2×C4 | semidirect |
| 28. C22⋊D193 | C2×C4 | semidirect |
| 30. C2×Dic193 | C2×C4 | semidirect |
| 35. C23×C193 | C2×C4 | semidirect |
| 61. C193 | #518 | semidirect |
| 69. C2×C22⋊C4 | D193 | semidirect |
| 78. C22×C4 | C2×D193 | semidirect |
| 84. C22⋊C4 | C2×D193 | semidirect |
| 90. C23 | C4×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D193 | 2 |
| C4×C22⋊D193 | 2 |
| #20259859 | 2 |
| #20259855 | 2 |
| C2×C22⋊Dic193 | 2 |
| C22⋊C4×D193 | 2 |
| C2×C22⋊C4×C193 | 2 |
| #518 | 193 |