Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#15690556 | C2 | semidirect |
| 2. C2×D4×D193 | C2 | semidirect |
| 3. #20259926 | C2 | direct (N × H) |
| 4. C2×#15690542 | C2 | semidirect |
| 5. C2×D1544 | C2 | semidirect |
| 6. C2×#15690540 | C2 | semidirect |
| 7. C2×#15690538 | C2 | semidirect |
| 8. C2×SD16×C193 | C2 | semidirect |
| 11. #15690556 | C22 | semidirect |
| 14. C2×D772 | C22 | semidirect |
| 17. D4×D193 | C22 | semidirect |
| 20. #15690542 | C22 | semidirect |
| 21. D1544 | C22 | semidirect |
| 22. #15690540 | C22 | semidirect |
| 23. #15690538 | C22 | semidirect |
| 24. C2×#13095393 | C22 | semidirect |
| 25. C2×Q8×C193 | C22 | semidirect |
| 27. SD16×C193 | C22 | semidirect |
| 28. C2×C8×C193 | C22 | semidirect |
| 38. D772 | C23 | semidirect |
| 44. #13095393 | C23 | semidirect |
| 47. Q8×C193 | C23 | semidirect |
| 52. C8×C193 | C23 | semidirect |
| 68. C2×C193 | AGL(1,ℤ/8) | semidirect |
| 73. C193 | C2×AGL(1,ℤ/8) | semidirect |
| 79. C2×SD16 | D193 | semidirect |
| 86. C2×Q8 | C2×D193 | semidirect |
| 97. SD16 | C2×D193 | semidirect |
| 102. C2×C8 | C2×D193 | semidirect |
| 110. Q8 | C22×D193 | semidirect |
| 126. C8 | C22×D193 | semidirect |
| 145. C2 | #20259926 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690556 | 2 |
| C2×D4×D193 | 2 |
| #20259926 | 2 |
| C2×#15690542 | 2 |
| C2×D1544 | 2 |
| C2×#15690540 | 2 |
| C2×#15690538 | 2 |
| C2×SD16×C193 | 2 |
| C2×AGL(1,ℤ/8) | 193 |