Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20259944 | C2 | semidirect |
| 2. #20259925 | C2 | semidirect |
| 3. #20259923 | C2 | semidirect |
| 4. #20259921 | C2 | semidirect |
| 5. #20259918 | C2 | semidirect |
| 6. D8×D193 | C2 | semidirect |
| 7. #20259905 | C2 | semidirect |
| 8. C2×D8×C193 | C2 | semidirect |
| 10. #15690555 | C22 | semidirect |
| 12. #15690554 | C22 | semidirect |
| 15. D4×D193 | C22 | semidirect |
| 16. Dic772 | C22 | semidirect |
| 17. #15690544 | C22 | semidirect |
| 18. #15690543 | C22 | semidirect |
| 19. D1544 | C22 | semidirect |
| 20. #15690540 | C22 | semidirect |
| 21. #15690539 | C22 | semidirect |
| 22. #15690538 | C22 | semidirect |
| 23. C8×D193 | C22 | semidirect |
| 24. C2×D4×C193 | C22 | semidirect |
| 25. D8×C193 | C22 | semidirect |
| 26. D8×C193 | C22 | semidirect |
| 27. C2×C8×C193 | C22 | semidirect |
| 62. C193 | #576 | semidirect |
| 70. C2×D8 | D193 | semidirect |
| 79. C2×D4 | C2×D193 | semidirect |
| 85. D8 | C2×D193 | semidirect |
| 86. D8 | C2×D193 | semidirect |
| 90. C2×C8 | C2×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259944 | 2 |
| #20259925 | 2 |
| #20259923 | 2 |
| #20259921 | 2 |
| #20259918 | 2 |
| D8×D193 | 2 |
| #20259905 | 2 |
| C2×D8×C193 | 2 |
| #576 | 193 |