Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20265732 | C2 | semidirect |
| 3. #20265482 | C2 | semidirect |
| 4. #20265476 | C2 | semidirect |
| 5. #20265472 | C2 | semidirect |
| 6. #20265468 | C2 | semidirect |
| 7. #20265454 | C2 | semidirect |
| 8. #20265212 | C2 | semidirect |
| 9. C4⋊C8×D101 | C2 | semidirect |
| 11. #475×C101 | C2 | semidirect |
| 44. #13108075 | Q8 | semidirect |
| 135. C101 | #3076 | semidirect |
| 142. #475 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265732 | 2 |
| C4×#13108075 | 2 |
| #20265482 | 2 |
| #20265476 | 2 |
| #20265472 | 2 |
| #20265468 | 2 |
| #20265454 | 2 |
| #20265212 | 2 |
| C4⋊C8×D101 | 2 |
| #20265172 | 2 |
| #475×C101 | 2 |
| #3076 | 101 |