Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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. #20266142 | C2 | semidirect |
| 3. C4×#13108084 | C2 | semidirect |
| 4. C4×D101⋊C8 | C2 | semidirect |
| 6. #15692343 | C4 | direct (N × H) |
| 20. #13108084 | C2×C4 | semidirect |
| 21. D101⋊C8 | C2×C4 | semidirect |
| 57. C4×C101 | #131 | semidirect |
| 59. Dic101 | #131 | semidirect |
| 66. C101 | C4×#131 | semidirect |
| 126. C4 | #15692343 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692343 | 2 |
| #20266142 | 2 |
| C4×#13108084 | 2 |
| C4×D101⋊C8 | 2 |
| C4×#13108075 | 2 |
| C4×#131 | 101 |