Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20265803 | C2 | semidirect |
| 4. #20264944 | C2 | semidirect |
| 5. #20264943 | C2 | semidirect |
| 6. #20264943 | C2 | semidirect |
| 36. C24×C101 | Q8 | semidirect |
| 46. C22×C4×C101 | Q8 | semidirect |
| 118. C101 | #2032 | semidirect |
| 139. C24 | Dic202 | semidirect |
| 154. C22×C4 | Dic202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265803 | 2 |
| C2×#15692170 | 2 |
| #20264944 | 2 |
| #20264943 | 2 |
| C2×#99×C101 | 2 |
| #2032 | 101 |