Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#15692278 | C2 | semidirect |
| 2. C2×#15692261 | C2 | semidirect |
| 3. #20265757 | C2 | semidirect |
| 4. #20265426 | C2 | semidirect |
| 5. #20265425 | C2 | semidirect |
| 6. #20265415 | C2 | semidirect |
| 7. #20265414 | C2 | semidirect |
| 8. #20265413 | C2 | semidirect |
| 9. #107×D101 | C2 | semidirect |
| 10. #20265177 | C2 | semidirect |
| 11. #467×C101 | C2 | semidirect |
| 65. C8×D101 | D4 | semidirect |
| 144. C101 | #3061 | semidirect |
| 151. #467 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C2×#15692261 | 2 |
| #20265757 | 2 |
| #20265426 | 2 |
| #20265425 | 2 |
| #20265415 | 2 |
| #20265414 | 2 |
| #20265413 | 2 |
| #107×D101 | 2 |
| #20265177 | 2 |
| #467×C101 | 2 |
| #3061 | 101 |