Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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. #20265832 | C2 | semidirect |
| 2. #20265529 | C2 | semidirect |
| 3. #20265518 | C2 | semidirect |
| 4. #20265464 | C2 | semidirect |
| 5. #20265404 | C2 | semidirect |
| 6. #20265382 | C2 | semidirect |
| 7. #20265320 | C2 | semidirect |
| 8. C4×#13108059 | C2 | semidirect |
| 9. D4×#11717579 | C2 | semidirect |
| 10. #20265171 | C2 | semidirect |
| 11. #555×C101 | C2 | semidirect |
| 131. C101 | #3303 | semidirect |
| 132. #555 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265832 | 2 |
| #20265529 | 2 |
| #20265518 | 2 |
| #20265464 | 2 |
| #20265404 | 2 |
| #20265382 | 2 |
| #20265320 | 2 |
| C4×#13108059 | 2 |
| D4×#11717579 | 2 |
| #20265171 | 2 |
| #555×C101 | 2 |
| #3303 | 101 |