Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20266255 | C2 | semidirect |
| 2. #20266175 | C2 | semidirect |
| 3. #20266169 | C2 | semidirect |
| 4. D101⋊#100 | C2 | semidirect |
| 5. #20266059 | C2 | semidirect |
| 6. #20266046 | C2 | semidirect |
| 22. C2×#13108063 | C4 | semidirect |
| 23. C2×#13108062 | C4 | semidirect |
| 24. C2×#13108059 | C4 | semidirect |
| 26. C2×D8×C101 | C4 | semidirect |
| 126. C101 | #1903 | semidirect |
| 141. C2×D8 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266255 | 2 |
| #20266175 | 2 |
| #20266169 | 2 |
| D101⋊#100 | 2 |
| #20266059 | 2 |
| #20266046 | 2 |
| C2×#15692279 | 2 |
| #1903 | 101 |