Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15692283 | C2 | semidirect |
| 2. #20265727 | C2 | semidirect |
| 3. C2×C4×D404 | C2 | semidirect |
| 4. #20265393 | C2 | semidirect |
| 5. #20265383 | C2 | semidirect |
| 6. #20265373 | C2 | semidirect |
| 7. #20265179 | C2 | semidirect |
| 8. #423×C101 | C2 | semidirect |
| 15. #15692255 | C22 | semidirect |
| 16. #15692252 | C22 | semidirect |
| 17. #15692243 | C22 | semidirect |
| 28. #15692180 | C22 | semidirect |
| 29. #15692177 | C22 | semidirect |
| 32. C4⋊C8×C101 | C22 | semidirect |
| 33. C4⋊C8×C101 | C22 | semidirect |
| 42. C2×D404 | D4 | semidirect |
| 118. C4×C101 | AGL(1,ℤ/8) | semidirect |
| 130. C101 | #3036 | semidirect |
| 137. #423 | D101 | semidirect |
| 160. C4⋊C8 | C2×D101 | semidirect |
| 161. C4⋊C8 | C2×D101 | semidirect |
| 250. C4 | #15692283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692283 | 2 |
| #20265727 | 2 |
| C2×C4×D404 | 2 |
| #20265393 | 2 |
| #20265383 | 2 |
| #20265373 | 2 |
| #20265179 | 2 |
| #423×C101 | 2 |
| #3036 | 101 |