Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 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×C22⋊#11715871 | C2 | semidirect |
| 2. #20259957 | C2 | direct (N × H) |
| 6. C22⋊#11715871 | C22 | semidirect |
| 10. C2×C22⋊D193 | C4 | semidirect |
| 12. C22×Dic193 | C4 | semidirect |
| 13. C24×C193 | C4 | semidirect |
| 25. C2×Dic193 | C2×C4 | semidirect |
| 30. C23×C193 | C2×C4 | semidirect |
| 50. C2×C193 | #99 | semidirect |
| 54. C193 | C2×#99 | semidirect |
| 60. C24 | #11715871 | semidirect |
| 78. C23 | C2×#11715871 | semidirect |
| 107. C2 | #20259957 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11715871 | 2 |
| #20259957 | 2 |
| C22×C22⋊D193 | 2 |
| C2×#99 | 193 |