Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 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. #20265734 | C2 | semidirect |
| 3. #20265478 | C2 | semidirect |
| 4. #20265468 | C2 | semidirect |
| 5. #20265458 | C2 | semidirect |
| 6. #20265219 | C2 | semidirect |
| 8. #423×C101 | C2 | semidirect |
| 11. #15692255 | C22 | semidirect |
| 12. #15692255 | C22 | semidirect |
| 13. #15692247 | C22 | semidirect |
| 25. #15692189 | C22 | semidirect |
| 26. #15692187 | C22 | semidirect |
| 31. C4⋊C8×C101 | C22 | semidirect |
| 32. C4⋊C8×C101 | C22 | semidirect |
| 38. C2×D404 | Q8 | semidirect |
| 116. C101 | #3077 | semidirect |
| 123. #423 | D101 | semidirect |
| 145. C4⋊C8 | C2×D101 | semidirect |
| 146. C4⋊C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265734 | 2 |
| C2×C4×D404 | 2 |
| #20265478 | 2 |
| #20265468 | 2 |
| #20265458 | 2 |
| #20265219 | 2 |
| #20265183 | 2 |
| #423×C101 | 2 |
| #3077 | 101 |