Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
774 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 204 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×#15692343 | C2 | semidirect |
| 2. #20266151 | C2 | semidirect |
| 3. #20266148 | C2 | semidirect |
| 4. D101⋊(C22⋊C8) | C2 | semidirect |
| 7. C2×#13108084 | C22 | semidirect |
| 8. C2×D101⋊C8 | C22 | semidirect |
| 11. C22⋊#11717581 | C22 | semidirect |
| 12. C22⋊#11717581 | C22 | semidirect |
| 77. C2×D101 | #131 | semidirect |
| 89. C101 | #2880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692343 | 2 |
| #20266151 | 2 |
| #20266148 | 2 |
| D101⋊(C22⋊C8) | 2 |
| C2×#41×D101 | 2 |
| #2880 | 101 |