Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
292 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 77 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⋊#11715906 | C2 | semidirect |
| 4. C2×C4×#11715906 | C2 | semidirect |
| 5. (C2×#11715906)⋊C4 | C2 | semidirect |
| 6. (C2×#11715906)⋊C4 | C2 | semidirect |
| 53. C22⋊Dic97 | C8 | semidirect |
| 54. #13095488 | C8 | semidirect |
| 55. #13095488 | C8 | semidirect |
| 56. C22⋊C4×C97 | C8 | semidirect |
| 135. C97 | #1923 | semidirect |
| 187. C22⋊C4 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715906 | 2 |
| C2×C22⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C22⋊C4×#87604 | 2 |
| #1923 | 97 |