Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#15692275 | C2 | semidirect |
| 2. #20265727 | C2 | semidirect |
| 3. #20265572 | C2 | semidirect |
| 4. #20265569 | C2 | semidirect |
| 5. #20265567 | C2 | semidirect |
| 6. #20265564 | C2 | semidirect |
| 7. C2×#15692166 | C2 | semidirect |
| 8. #532×C101 | C2 | semidirect |
| 40. C2×#11717579 | D4 | semidirect |
| 98. C101 | #3150 | semidirect |
| 101. #532 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692275 | 2 |
| #20265727 | 2 |
| #20265572 | 2 |
| #20265569 | 2 |
| #20265567 | 2 |
| #20265564 | 2 |
| C2×#15692166 | 2 |
| #532×C101 | 2 |
| #3150 | 101 |