Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20265805 | C2 | semidirect |
| 3. #20265478 | C2 | semidirect |
| 4. #20265478 | C2 | semidirect |
| 5. #20265468 | C2 | semidirect |
| 6. #20265458 | C2 | semidirect |
| 7. #20265219 | C2 | semidirect |
| 8. #20265215 | C2 | semidirect |
| 11. #424×C101 | C2 | semidirect |
| 13. #15692255 | C22 | semidirect |
| 15. #15692247 | C22 | semidirect |
| 26. #15692189 | C22 | semidirect |
| 27. #15692189 | C22 | semidirect |
| 28. #15692189 | C22 | semidirect |
| 29. #15692187 | C22 | semidirect |
| 30. #15692187 | C22 | semidirect |
| 31. #15692187 | C22 | semidirect |
| 39. C4⋊C8×C101 | C22 | semidirect |
| 40. C4⋊C8×C101 | C22 | semidirect |
| 45. C2×D404 | Q8 | semidirect |
| 125. C101 | #3081 | semidirect |
| 134. #424 | D101 | semidirect |
| 160. C4⋊C8 | C2×D101 | semidirect |
| 161. C4⋊C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265805 | 2 |
| #20265651 | 2 |
| #20265478 | 2 |
| #20265468 | 2 |
| #20265458 | 2 |
| #20265219 | 2 |
| #20265215 | 2 |
| #20265183 | 2 |
| C2×#15692177 | 2 |
| #424×C101 | 2 |
| #3081 | 101 |