Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#15692212 | C2 | semidirect |
| 3. C2×C4⋊C4×D101 | C2 | semidirect |
| 4. #20265083 | C2 | semidirect |
| 5. #20265082 | C2 | semidirect |
| 6. #20265080 | C2 | semidirect |
| 7. #20265053 | C2 | semidirect |
| 8. #20265035 | C2 | semidirect |
| 9. #390×C101 | C2 | semidirect |
| 12. C2×#13108073 | C4 | semidirect |
| 36. C2×Dic202 | C2×C4 | semidirect |
| 42. C22×Dic101 | C2×C4 | semidirect |
| 61. C2×D4×C101 | C2×C4 | semidirect |
| 102. C4×D101 | C22⋊C4 | semidirect |
| 134. C101 | #2311 | semidirect |
| 141. #390 | D101 | semidirect |
| 177. C2×D4 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C2×#15692212 | 2 |
| C2×C4⋊C4×D101 | 2 |
| #20265083 | 2 |
| #20265082 | 2 |
| #20265080 | 2 |
| #20265053 | 2 |
| #20265035 | 2 |
| #390×C101 | 2 |
| #2311 | 101 |