Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20265072 | C2 | semidirect |
| 3. #20265071 | C2 | semidirect |
| 4. #20265065 | C2 | semidirect |
| 5. #20265061 | C2 | semidirect |
| 7. #20265049 | C2 | semidirect |
| 8. #20265035 | C2 | semidirect |
| 12. #15692236 | C4 | semidirect |
| 36. C22×Dic101 | C2×C4 | semidirect |
| 44. #13108053 | C2×C4 | semidirect |
| 48. C22⋊Dic101 | C2×C4 | semidirect |
| 127. C101 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692236 | 2 |
| #20265072 | 2 |
| #20265071 | 2 |
| #20265065 | 2 |
| #20265061 | 2 |
| #20265057 | 2 |
| #20265049 | 2 |
| #20265035 | 2 |
| #390×C101 | 2 |
| #2376 | 101 |