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. #20259945 | C2 | semidirect |
| 2. #20259930 | C2 | semidirect |
| 3. #20259924 | C2 | semidirect |
| 4. #20259919 | C2 | semidirect |
| 5. C2×#15690542 | C2 | semidirect |
| 6. #20259906 | C2 | semidirect |
| 7. 2−1+4×C193 | C2 | semidirect |
| 12. #15690545 | C22 | semidirect |
| 13. #15690543 | C22 | semidirect |
| 14. #15690542 | C22 | semidirect |
| 15. #15690542 | C22 | semidirect |
| 16. #15690540 | C22 | semidirect |
| 17. #15690539 | C22 | semidirect |
| 18. C2×#13095393 | C22 | semidirect |
| 21. #41×C193 | C22 | semidirect |
| 23. C2×Q8×C193 | C22 | semidirect |
| 53. C193 | #577 | semidirect |
| 55. 2−1+4 | D193 | semidirect |
| 66. #41 | C2×D193 | semidirect |
| 68. C2×Q8 | C2×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259945 | 2 |
| #20259930 | 2 |
| #20259924 | 2 |
| #20259919 | 2 |
| C2×#15690542 | 2 |
| #20259906 | 2 |
| 2−1+4×C193 | 2 |
| #577 | 193 |