Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
488 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 194 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. #20266199 | C2 | direct (N × H) |
| 2. C2×C4⋊#11717581 | C2 | semidirect |
| 4. C2×#15692310 | C2 | semidirect |
| 7. C4⋊#11717581 | C22 | semidirect |
| 9. #15692310 | C22 | semidirect |
| 79. C2×C101 | #432 | semidirect |
| 85. C101 | C2×#432 | semidirect |
| 165. C2 | #20266199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266199 | 2 |
| C2×C4⋊#11717581 | 2 |
| C2×#15692312 | 2 |
| C2×#15692310 | 2 |
| C2×C42×D101 | 2 |
| C2×#432 | 101 |