Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
588 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20266175 | C2 | semidirect |
| 2. #20266169 | C2 | semidirect |
| 3. #20266163 | C2 | semidirect |
| 4. #20266156 | C2 | semidirect |
| 6. D101⋊M16 | C22 | semidirect |
| 7. #15692334 | C22 | semidirect |
| 16. C2×#13108074 | C4 | semidirect |
| 19. C2×#13108073 | C4 | semidirect |
| 24. C2×D4×D101 | C4 | semidirect |
| 26. C22×D4×C101 | C4 | semidirect |
| 152. C101 | #1795 | semidirect |
| 170. C22×D4 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266175 | 2 |
| #20266169 | 2 |
| #20266163 | 2 |
| #20266156 | 2 |
| C2×#15692300 | 2 |
| #1795 | 101 |