Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #20265073 | C2 | semidirect |
| 5. #20265046 | C2 | semidirect |
| 6. #20265042 | C2 | semidirect |
| 9. #15692214 | C4 | semidirect |
| 29. C4⋊Dic101 | C2×C4 | semidirect |
| 34. C4×Dic101 | C2×C4 | semidirect |
| 55. C2×C4×C101 | C4⋊C4 | semidirect |
| 92. C101 | #2317 | semidirect |
| 154. C2×C4 | #13108053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692214 | 2 |
| #20265073 | 2 |
| #20265050 | 2 |
| #20265046 | 2 |
| #20265042 | 2 |
| C22×C4⋊C4×C101 | 2 |
| #2317 | 101 |