Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C2×C4×#11715871 | C2 | semidirect |
| 3. (C2×#11715871)⋊C4 | C2 | semidirect |
| 6. C22⋊#11715871 | C4 | direct (N × H) |
| 9. C22×Dic193 | C4 | semidirect |
| 11. C2×C4×D193 | C4 | semidirect |
| 12. C2×C4×D193 | C4 | semidirect |
| 15. C22×C4×C193 | C4 | semidirect |
| 18. C2×#11715871 | C2×C4 | semidirect |
| 37. C22×C193 | C42 | semidirect |
| 42. C2×D193 | C42 | semidirect |
| 48. C4×C193 | C22⋊C4 | semidirect |
| 50. Dic193 | C22⋊C4 | semidirect |
| 57. C193 | C4×C22⋊C4 | semidirect |
| 71. C22×C4 | #11715871 | semidirect |
| 102. C22 | C4×#11715871 | semidirect |
| 108. C4 | C22⋊#11715871 | 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 |
| C2×C4×#11715871 | 2 |
| (C2×#11715871)⋊C4 | 2 |
| C22×C4×D193 | 2 |
| C4×C22⋊C4 | 193 |