Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 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×Dic386 | C2 | semidirect |
| 3. #20259864 | C2 | semidirect |
| 4. D4×Dic193 | C2 | semidirect |
| 5. C4×C22⋊D193 | C2 | semidirect |
| 6. #20259859 | C2 | semidirect |
| 7. #20259856 | C2 | semidirect |
| 8. #20259855 | C2 | semidirect |
| 9. C2×#15690534 | C2 | semidirect |
| 10. C4⋊C4×D193 | C2 | semidirect |
| 11. C4×D4×C193 | C2 | semidirect |
| 12. #15690554 | C4 | semidirect |
| 37. Dic386 | C2×C4 | semidirect |
| 38. C22⋊D193 | C2×C4 | semidirect |
| 40. C2×Dic193 | C2×C4 | semidirect |
| 47. C4×D193 | C2×C4 | semidirect |
| 49. D4×C193 | C2×C4 | semidirect |
| 76. C193 | #520 | semidirect |
| 84. C4×D4 | D193 | semidirect |
| 117. D4 | C4×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690554 | 2 |
| C4×Dic386 | 2 |
| #20259864 | 2 |
| D4×Dic193 | 2 |
| C4×C22⋊D193 | 2 |
| #20259859 | 2 |
| #20259856 | 2 |
| #20259855 | 2 |
| C2×#15690534 | 2 |
| C4⋊C4×D193 | 2 |
| C4×D4×C193 | 2 |
| #520 | 193 |