Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #20259946 | C2 | semidirect |
| 2. #20259945 | C2 | semidirect |
| 3. #20259932 | C2 | semidirect |
| 4. #20259927 | C2 | semidirect |
| 5. #20259921 | C2 | semidirect |
| 6. C2×#15690544 | C2 | semidirect |
| 7. #131×C193 | C2 | semidirect |
| 10. #15690555 | C22 | semidirect |
| 12. C2×Dic386 | C22 | semidirect |
| 16. Dic772 | C22 | semidirect |
| 17. #15690544 | C22 | semidirect |
| 18. #15690544 | C22 | semidirect |
| 19. #15690544 | C22 | semidirect |
| 20. D1544 | C22 | semidirect |
| 22. M16×C193 | C22 | semidirect |
| 23. C2×C8×C193 | C22 | semidirect |
| 53. C193 | #577 | semidirect |
| 61. #131 | D193 | semidirect |
| 76. M16 | C2×D193 | semidirect |
| 77. C2×C8 | C2×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259946 | 2 |
| #20259945 | 2 |
| #20259932 | 2 |
| #20259927 | 2 |
| #20259921 | 2 |
| C2×#15690544 | 2 |
| #131×C193 | 2 |
| #577 | 193 |