Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20265077 | C2 | semidirect |
| 3. #20265066 | C2 | semidirect |
| 4. #20265062 | C2 | semidirect |
| 5. #20265055 | C2 | semidirect |
| 6. #20265053 | C2 | semidirect |
| 7. C4×C22⋊Dic101 | C2 | semidirect |
| 8. #20265024 | C2 | semidirect |
| 9. #381×C101 | C2 | semidirect |
| 13. #15692229 | C4 | semidirect |
| 38. C2×C22⋊D101 | C2×C4 | semidirect |
| 45. C4⋊Dic101 | C2×C4 | semidirect |
| 51. #13108051 | C2×C4 | semidirect |
| 58. C22×C4×C101 | C2×C4 | semidirect |
| 135. C101 | #2333 | semidirect |
| 142. #381 | D101 | semidirect |
| 183. C22×C4 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692229 | 2 |
| #20265077 | 2 |
| #20265066 | 2 |
| #20265062 | 2 |
| #20265055 | 2 |
| #20265053 | 2 |
| C4×C22⋊Dic101 | 2 |
| #20265024 | 2 |
| #381×C101 | 2 |
| #2333 | 101 |