Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 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. #20266204 | C2 | semidirect |
| 2. #20266194 | C2 | semidirect |
| 3. D101⋊(C22⋊C8) | C2 | semidirect |
| 4. C2×C22⋊#11717581 | C2 | semidirect |
| 6. C2×D101⋊C8 | C22 | semidirect |
| 7. C22×#11717581 | C22 | semidirect |
| 8. #15692322 | C22 | semidirect |
| 9. #15692312 | C22 | semidirect |
| 11. C22⋊#11717581 | C22 | semidirect |
| 12. C4×#11717581 | C22 | semidirect |
| 26. C2×C22⋊D101 | C8 | semidirect |
| 47. C23×C101 | C2×C8 | semidirect |
| 52. C22×D101 | C2×C8 | semidirect |
| 58. C22⋊D101 | C2×C8 | semidirect |
| 63. C2×Dic101 | C2×C8 | semidirect |
| 96. C101 | #2972 | semidirect |
| 147. C23 | D101⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266204 | 2 |
| #20266194 | 2 |
| D101⋊(C22⋊C8) | 2 |
| C2×C22⋊#11717581 | 2 |
| C2×#15692215 | 2 |
| #2972 | 101 |