Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692277 | C2 | semidirect |
| 2. #20265688 | C2 | semidirect |
| 3. #20265435 | C2 | semidirect |
| 4. #20265430 | C2 | semidirect |
| 5. #20265423 | C2 | semidirect |
| 6. #20265215 | C2 | semidirect |
| 7. #20265174 | C2 | semidirect |
| 8. C22×M16×C101 | C2 | semidirect |
| 11. C2×Dic404 | C22 | semidirect |
| 12. C2×#13108063 | C22 | semidirect |
| 13. C2×D808 | C22 | semidirect |
| 20. #15692189 | C22 | semidirect |
| 21. #15692187 | C22 | semidirect |
| 22. #15692180 | C22 | semidirect |
| 23. #15692177 | C22 | semidirect |
| 56. C2×C8×C101 | D4 | semidirect |
| 106. C101 | #3054 | semidirect |
| 108. C22×M16 | D101 | semidirect |
| 156. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| #20265688 | 2 |
| #20265435 | 2 |
| #20265430 | 2 |
| #20265423 | 2 |
| #20265215 | 2 |
| #20265174 | 2 |
| C22×M16×C101 | 2 |
| #3054 | 101 |