Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×#13108063 | C2 | semidirect |
| 3. C2×#15692177 | C2 | semidirect |
| 4. #20265083 | C2 | semidirect |
| 5. #336×C101 | C2 | semidirect |
| 22. C2×Dic202 | D4 | semidirect |
| 40. C2×C8×C101 | D4 | semidirect |
| 50. C2×C4×C101 | SD16 | semidirect |
| 90. C101 | #2014 | semidirect |
| 95. #336 | D101 | semidirect |
| 129. C2×C8 | D404 | semidirect |
| 152. C2×C4 | #13108063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108063 | 2 |
| C2×#15692252 | 2 |
| C2×#15692177 | 2 |
| #20265083 | 2 |
| #336×C101 | 2 |
| #2014 | 101 |