Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265897 | C2 | semidirect |
| 3. #20265528 | C2 | semidirect |
| 4. #20265519 | C2 | semidirect |
| 5. #20265458 | C2 | semidirect |
| 6. #20265418 | C2 | semidirect |
| 7. #20265388 | C2 | semidirect |
| 8. #20265341 | C2 | semidirect |
| 9. C4×#13108063 | C2 | semidirect |
| 10. #20265174 | C2 | semidirect |
| 11. C8×D4×C101 | C2 | semidirect |
| 126. C101 | #3302 | semidirect |
| 136. C8×D4 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265897 | 2 |
| #20265832 | 2 |
| #20265528 | 2 |
| #20265519 | 2 |
| #20265458 | 2 |
| #20265418 | 2 |
| #20265388 | 2 |
| #20265341 | 2 |
| C4×#13108063 | 2 |
| #20265174 | 2 |
| C8×D4×C101 | 2 |
| #3302 | 101 |