Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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×#15692186 | C2 | semidirect |
| 5. #20264939 | C2 | semidirect |
| 6. #20264932 | C2 | semidirect |
| 7. #389×C101 | C2 | semidirect |
| 18. #15692175 | C4 | semidirect |
| 40. C2×#11717579 | C2×C4 | semidirect |
| 53. C4⋊C4×C101 | C2×C4 | semidirect |
| 88. D404 | C4⋊C4 | semidirect |
| 124. C101 | #1864 | semidirect |
| 129. #389 | D101 | semidirect |
| 176. C4⋊C4 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D404 | 2 |
| C2×#15692186 | 2 |
| C2×#15692175 | 2 |
| #20264939 | 2 |
| #20264932 | 2 |
| #389×C101 | 2 |
| #1864 | 101 |