Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
936 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 285 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×#15692214 | C2 | semidirect |
| 3. #20265083 | C2 | semidirect |
| 4. #20265079 | C2 | semidirect |
| 5. #20265056 | C2 | semidirect |
| 6. C4×#13108051 | C2 | semidirect |
| 7. C22×C42×C101 | C2 | semidirect |
| 10. C2×#13108074 | C4 | semidirect |
| 30. C2×Dic202 | C2×C4 | semidirect |
| 33. C2×D404 | C2×C4 | semidirect |
| 41. C2×C4×D101 | C2×C4 | semidirect |
| 69. C2×C4×C101 | C22⋊C4 | semidirect |
| 76. C2×C4×C101 | #41 | semidirect |
| 110. C101 | #2297 | semidirect |
| 113. C22×C42 | D101 | semidirect |
| 188. C2×C4 | #13108051 | semidirect |
| 195. 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×#15692214 | 2 |
| #20265083 | 2 |
| #20265079 | 2 |
| #20265056 | 2 |
| C4×#13108051 | 2 |
| C22×C42×C101 | 2 |
| #2297 | 101 |