Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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×#15692200 | C2 | semidirect |
| 3. C2×#15692199 | C2 | semidirect |
| 4. #20265419 | C2 | semidirect |
| 5. #20264977 | C2 | semidirect |
| 6. #20264956 | C2 | semidirect |
| 7. #357×C101 | C2 | semidirect |
| 9. C2×Dic404 | C22 | semidirect |
| 18. C2×#13108049 | C22 | semidirect |
| 21. C2×C16×C101 | C22 | semidirect |
| 22. #107×C101 | C22 | semidirect |
| 79. C2×D101 | SD32 | semidirect |
| 92. C101 | #2187 | semidirect |
| 98. #357 | D101 | semidirect |
| 112. C2×C16 | C2×D101 | semidirect |
| 113. #107 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D101 | 2 |
| C2×#15692200 | 2 |
| C2×#15692199 | 2 |
| #20265419 | 2 |
| #20264977 | 2 |
| #20264956 | 2 |
| #357×C101 | 2 |
| #2187 | 101 |