Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#15692220 | C2 | semidirect |
| 4. #20265082 | C2 | semidirect |
| 6. #20265067 | C2 | semidirect |
| 7. #20265048 | C2 | semidirect |
| 8. #20265023 | C2 | semidirect |
| 9. #384×C101 | C2 | semidirect |
| 13. #15692243 | C4 | semidirect |
| 33. C2×Dic202 | C2×C4 | semidirect |
| 46. #13108051 | C2×C4 | semidirect |
| 57. C42×C101 | C2×C4 | semidirect |
| 112. C101 | #2326 | semidirect |
| 120. #384 | D101 | semidirect |
| 169. C42 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692243 | 2 |
| C2×#15692220 | 2 |
| C2×#15692217 | 2 |
| #20265082 | 2 |
| #20265078 | 2 |
| #20265067 | 2 |
| #20265048 | 2 |
| #20265023 | 2 |
| #384×C101 | 2 |
| #2326 | 101 |