Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 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. #20265897 | C2 | semidirect |
| 3. #20265582 | C2 | semidirect |
| 4. #20265513 | C2 | semidirect |
| 5. #20265502 | C2 | semidirect |
| 6. #20265463 | C2 | semidirect |
| 7. #20265458 | C2 | semidirect |
| 8. #20265423 | C2 | semidirect |
| 9. C4×#13108063 | C2 | semidirect |
| 10. #20265219 | C2 | semidirect |
| 11. #436×C101 | C2 | semidirect |
| 99. C8×C101 | #41 | semidirect |
| 123. C101 | #3353 | semidirect |
| 133. #436 | D101 | semidirect |
| 222. C8 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265897 | 2 |
| #20265831 | 2 |
| #20265582 | 2 |
| #20265513 | 2 |
| #20265502 | 2 |
| #20265463 | 2 |
| #20265458 | 2 |
| #20265423 | 2 |
| C4×#13108063 | 2 |
| #20265219 | 2 |
| #436×C101 | 2 |
| #3353 | 101 |