Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
436 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11715906 | C2 | semidirect |
| 3. (C2×#11715906)⋊C4 | C2 | semidirect |
| 6. C22⋊#11715906 | C4 | direct (N × H) |
| 18. C2×#11715906 | C2×C4 | semidirect |
| 23. C22×#87604 | C8 | semidirect |
| 34. C22×Dic97 | C8 | semidirect |
| 37. C2×C4×D97 | C8 | semidirect |
| 38. C2×C4×D97 | C8 | semidirect |
| 41. C22×C4×C97 | C8 | semidirect |
| 80. C22×C97 | C4×C8 | semidirect |
| 88. C2×D97 | C4×C8 | semidirect |
| 97. #87604 | C22⋊C8 | semidirect |
| 100. C4×C97 | C22⋊C8 | semidirect |
| 102. Dic97 | C22⋊C8 | semidirect |
| 113. C97 | C4×C22⋊C8 | semidirect |
| 147. C22×C4 | #11715906 | semidirect |
| 206. C22 | C4×#11715906 | semidirect |
| 215. C4 | C22⋊#11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C22×C4×#87604 | 2 |
| C4×C22⋊C8 | 97 |