Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×Dic202 | C2 | semidirect |
| 3. #20265082 | C2 | semidirect |
| 5. #20265065 | C2 | semidirect |
| 6. #20265050 | C2 | semidirect |
| 7. #20265046 | C2 | semidirect |
| 8. #20265023 | C2 | semidirect |
| 11. #15692242 | C4 | semidirect |
| 32. C2×Dic202 | C2×C4 | semidirect |
| 41. C22⋊Dic101 | C2×C4 | semidirect |
| 44. C4×Dic101 | C2×C4 | semidirect |
| 112. C101 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692242 | 2 |
| C2×C4×Dic202 | 2 |
| #20265082 | 2 |
| #20265080 | 2 |
| #20265065 | 2 |
| #20265050 | 2 |
| #20265046 | 2 |
| #20265023 | 2 |
| C2×C4×D4×C101 | 2 |
| #2326 | 101 |