Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
872 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 237 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×C4×Dic202 | C2 | semidirect |
| 3. #20265079 | C2 | semidirect |
| 4. #20265077 | C2 | semidirect |
| 5. #20265037 | C2 | semidirect |
| 6. #20265036 | C2 | semidirect |
| 7. #20265024 | C2 | semidirect |
| 8. C4×C22⋊C4×C101 | C2 | semidirect |
| 10. C2×#13108074 | C4 | semidirect |
| 76. C2×C4×C101 | #41 | semidirect |
| 85. Dic202 | C22⋊C4 | semidirect |
| 115. C101 | #2341 | semidirect |
| 123. C4×C22⋊C4 | D101 | semidirect |
| 200. C2×C4 | #13108074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108074 | 2 |
| C2×C4×Dic202 | 2 |
| #20265079 | 2 |
| #20265077 | 2 |
| #20265037 | 2 |
| #20265036 | 2 |
| #20265024 | 2 |
| C4×C22⋊C4×C101 | 2 |
| #2341 | 101 |