Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265734 | C2 | semidirect |
| 3. #20265519 | C2 | semidirect |
| 4. #20265473 | C2 | semidirect |
| 5. #20265468 | C2 | semidirect |
| 6. #20265388 | C2 | semidirect |
| 7. #20265383 | C2 | semidirect |
| 9. #20265285 | C2 | semidirect |
| 10. #20265279 | C2 | semidirect |
| 11. #432×C101 | C2 | semidirect |
| 137. C101 | #3116 | semidirect |
| 148. #432 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265734 | 2 |
| C4×#13108074 | 2 |
| #20265519 | 2 |
| #20265473 | 2 |
| #20265468 | 2 |
| #20265388 | 2 |
| #20265383 | 2 |
| #20265341 | 2 |
| #20265285 | 2 |
| #20265279 | 2 |
| #432×C101 | 2 |
| #3116 | 101 |