Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#15690555 | C2 | semidirect |
| 2. #20259930 | C2 | semidirect |
| 3. #20259929 | C2 | semidirect |
| 4. #20259925 | C2 | semidirect |
| 5. #20259924 | C2 | semidirect |
| 6. #20259919 | C2 | semidirect |
| 7. C2×#15690539 | C2 | semidirect |
| 8. C2×#41×C193 | C2 | semidirect |
| 12. #15690555 | C22 | semidirect |
| 13. C2×Dic386 | C22 | semidirect |
| 14. C2×D772 | C22 | semidirect |
| 17. #15690545 | C22 | semidirect |
| 18. #15690543 | C22 | semidirect |
| 19. #15690542 | C22 | semidirect |
| 20. #15690540 | C22 | semidirect |
| 21. #15690539 | C22 | semidirect |
| 22. #15690539 | C22 | semidirect |
| 23. C2×#13095393 | C22 | semidirect |
| 27. #41×C193 | C22 | semidirect |
| 28. C2×Q8×C193 | C22 | semidirect |
| 30. C2×D4×C193 | C22 | semidirect |
| 81. C193 | #575 | semidirect |
| 84. C2×#41 | D193 | semidirect |
| 98. #41 | C2×D193 | semidirect |
| 100. C2×Q8 | C2×D193 | semidirect |
| 104. C2×D4 | C2×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690555 | 2 |
| #20259930 | 2 |
| #20259929 | 2 |
| #20259925 | 2 |
| #20259924 | 2 |
| #20259919 | 2 |
| C2×#15690539 | 2 |
| C2×#41×C193 | 2 |
| #575 | 193 |