Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15692285 | C2 | semidirect |
| 2. C2×C4×Dic202 | C2 | semidirect |
| 3. #20265396 | C2 | semidirect |
| 4. #20265384 | C2 | semidirect |
| 5. #20265374 | C2 | semidirect |
| 6. #20265201 | C2 | semidirect |
| 7. #20265178 | C2 | semidirect |
| 36. C2×Dic202 | D4 | semidirect |
| 110. C4×C101 | #137 | semidirect |
| 121. C101 | #3037 | semidirect |
| 233. C4 | #15692285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692285 | 2 |
| C2×C4×Dic202 | 2 |
| #20265396 | 2 |
| #20265384 | 2 |
| #20265374 | 2 |
| #20265201 | 2 |
| #20265178 | 2 |
| #532×C101 | 2 |
| #3037 | 101 |