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. #20259963 | C2 | direct (N × H) |
| 7. #15690565 | C22 | semidirect |
| 10. C4×#11715871 | C22 | semidirect |
| 13. #15690554 | C4 | semidirect |
| 15. C2×Dic386 | C4 | semidirect |
| 19. C2×D4×C193 | C4 | semidirect |
| 25. Dic386 | C2×C4 | semidirect |
| 38. D4×C193 | C2×C4 | semidirect |
| 53. C2×C193 | #104 | semidirect |
| 57. C193 | C2×#104 | semidirect |
| 69. C2×D4 | #11715871 | semidirect |
| 85. D4 | C2×#11715871 | semidirect |
| 113. C2 | #20259963 | 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 |
| #20259963 | 2 |
| C2×#15690554 | 2 |
| C2×#104 | 193 |