Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic202 | C2 | semidirect |
| 2. C2×#15692285 | C2 | semidirect |
| 3. #20265332 | C2 | semidirect |
| 4. #20265315 | C2 | semidirect |
| 5. #20265185 | C2 | semidirect |
| 6. #20265141 | C2 | semidirect |
| 15. C2×#13108064 | C22 | semidirect |
| 16. C2×#13108062 | C22 | semidirect |
| 18. #15692178 | C22 | semidirect |
| 34. C2×Dic202 | D4 | semidirect |
| 95. C22×C101 | #137 | semidirect |
| 109. C101 | #3004 | semidirect |
| 204. C22 | #15692285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic202 | 2 |
| C2×#15692285 | 2 |
| #20265332 | 2 |
| #20265315 | 2 |
| #20265185 | 2 |
| #20265141 | 2 |
| #525×C101 | 2 |
| #3004 | 101 |