Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
344 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
| 2. C2×C4×#11715906 | C2 | semidirect |
| 3. D4⋊#11715906 | C2 | direct (N × H) |
| 8. C4⋊#11715906 | C22 | semidirect |
| 10. C4×#11715906 | C22 | semidirect |
| 40. C2×D388 | C8 | semidirect |
| 44. D4×D97 | C8 | semidirect |
| 47. C2×D4×C97 | C8 | semidirect |
| 70. D4×C97 | C2×C8 | semidirect |
| 76. D388 | C2×C8 | semidirect |
| 104. C2×C97 | D4⋊C8 | semidirect |
| 107. D97 | D4⋊C8 | semidirect |
| 111. C97 | C2×D4⋊C8 | semidirect |
| 138. C2×D4 | #11715906 | semidirect |
| 171. D4 | C2×#11715906 | semidirect |
| 219. C2 | D4⋊#11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| D4⋊#11715906 | 2 |
| C2×D4×#87604 | 2 |
| C2×D4⋊C8 | 97 |