Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| 3. (C2×#11715906)⋊C4 | C2 | semidirect |
| 35. C22×Dic97 | C8 | semidirect |
| 38. C2×C4×D97 | C8 | semidirect |
| 39. C2×C4×D97 | C8 | semidirect |
| 42. C22×C4×C97 | C8 | semidirect |
| 83. C22×C97 | C4⋊C8 | semidirect |
| 91. C2×D97 | C4⋊C8 | semidirect |
| 104. C4×C97 | C22⋊C8 | semidirect |
| 106. Dic97 | C22⋊C8 | semidirect |
| 117. C97 | #1797 | semidirect |
| 152. C22×C4 | #11715906 | semidirect |
| 213. C22 | C4⋊#11715906 | semidirect |
| 223. C4 | C22⋊#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×#11715906)⋊C4 | 2 |
| C22×C4×#87604 | 2 |
| #1797 | 97 |