Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
122 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 44 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. Q8×#11715871 | C2 | semidirect |
| 3. #20259967 | C2 | semidirect |
| 4. #20259962 | C2 | semidirect |
| 6. C8×#11715871 | C2 | semidirect |
| 18. #15690544 | C4 | semidirect |
| 19. #15690543 | C4 | semidirect |
| 20. #15690542 | C4 | semidirect |
| 22. SD16×C193 | C4 | semidirect |
| 31. Dic386 | C2×C4 | semidirect |
| 36. #13095393 | C2×C4 | semidirect |
| 37. Q8×C193 | C2×C4 | semidirect |
| 39. C8×C193 | C2×C4 | semidirect |
| 48. #11715871 | SD16 | direct (N × H) |
| 58. C193 | C4×SD16 | semidirect |
| 73. SD16 | #11715871 | direct (N × H) |
| 85. Q8 | C2×#11715871 | semidirect |
| 98. C8 | C2×#11715871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715871 | 2 |
| D4×#11715871 | 2 |
| #20259967 | 2 |
| #20259962 | 2 |
| #20259961 | 2 |
| C8×#11715871 | 2 |
| SD16×D193 | 2 |
| C4×SD16 | 193 |