Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
688 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#15692238 | C2 | semidirect |
| 3. C22×C4×Dic101 | C2 | semidirect |
| 4. #20265077 | C2 | semidirect |
| 5. #20265072 | C2 | semidirect |
| 6. #20265071 | C2 | semidirect |
| 7. #20265067 | C2 | semidirect |
| 8. #20265057 | C2 | semidirect |
| 9. #20265054 | C2 | semidirect |
| 10. #20265035 | C2 | semidirect |
| 11. C2×#123×C101 | C2 | semidirect |
| 72. C22×C4×C101 | D4 | semidirect |
| 150. Dic101 | #123 | semidirect |
| 160. C101 | #2854 | semidirect |
| 162. C2×#123 | D101 | semidirect |
| 221. C22×C4 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692238 | 2 |
| C2×#15692227 | 2 |
| C22×C4×Dic101 | 2 |
| #20265077 | 2 |
| #20265072 | 2 |
| #20265071 | 2 |
| #20265067 | 2 |
| #20265057 | 2 |
| #20265054 | 2 |
| #20265035 | 2 |
| C2×#123×C101 | 2 |
| #2854 | 101 |