Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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×#15690565 | C2 | semidirect |
| 2. C2×C4×#11715871 | C2 | semidirect |
| 3. #20259964 | C2 | direct (N × H) |
| 7. #15690565 | C22 | semidirect |
| 10. C4×#11715871 | C22 | semidirect |
| 13. #15690556 | C4 | semidirect |
| 16. C2×D772 | C4 | semidirect |
| 19. C2×Q8×C193 | C4 | semidirect |
| 28. D772 | C2×C4 | semidirect |
| 37. Q8×C193 | C2×C4 | semidirect |
| 52. C2×C193 | #104 | semidirect |
| 57. C193 | C2×#104 | semidirect |
| 67. C2×Q8 | #11715871 | semidirect |
| 81. Q8 | C2×#11715871 | semidirect |
| 113. C2 | #20259964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690565 | 2 |
| C2×C4×#11715871 | 2 |
| #20259964 | 2 |
| C2×#15690556 | 2 |
| C2×#104 | 193 |