Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
258 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 64 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×C4⋊#11715871 | C2 | semidirect |
| 2. C2×C22⋊#11715871 | C2 | semidirect |
| 3. C2×C4×#11715871 | C2 | semidirect |
| 11. C2×D772 | C4 | semidirect |
| 12. C2×C22⋊D193 | C4 | semidirect |
| 16. C2×D4×C193 | C4 | semidirect |
| 21. C2×#11715871 | D4 | semidirect |
| 50. C4×C193 | C22⋊C4 | semidirect |
| 51. Dic193 | C22⋊C4 | semidirect |
| 59. C193 | #390 | semidirect |
| 70. C2×D4 | #11715871 | semidirect |
| 111. C4 | C22⋊#11715871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715871 | 2 |
| C2×C22⋊#11715871 | 2 |
| C2×C4×#11715871 | 2 |
| C2×D4×D193 | 2 |
| #390 | 193 |