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 |
|---|---|---|
| 2. #20265474 | C2 | semidirect |
| 3. #20265474 | C2 | semidirect |
| 4. #20265464 | C2 | semidirect |
| 5. #20265454 | C2 | semidirect |
| 6. #20265217 | C2 | semidirect |
| 7. #20265213 | C2 | semidirect |
| 8. #20265204 | C2 | semidirect |
| 11. #544×C101 | C2 | semidirect |
| 21. #15692188 | C22 | semidirect |
| 22. #15692188 | C22 | semidirect |
| 23. #15692188 | C22 | semidirect |
| 24. #15692186 | C22 | semidirect |
| 25. #15692186 | C22 | semidirect |
| 26. #15692186 | C22 | semidirect |
| 27. C4⋊#11717579 | C22 | semidirect |
| 28. C4⋊#11717579 | C22 | semidirect |
| 34. C4⋊Q8×C101 | C22 | semidirect |
| 36. #125×C101 | C22 | semidirect |
| 44. C2×D404 | Q8 | semidirect |
| 125. C101 | #3081 | semidirect |
| 126. #544 | D101 | semidirect |
| 141. C4⋊Q8 | C2×D101 | semidirect |
| 143. #125 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265651 | 2 |
| #20265474 | 2 |
| #20265464 | 2 |
| #20265454 | 2 |
| #20265217 | 2 |
| #20265213 | 2 |
| #20265204 | 2 |
| #20265181 | 2 |
| C2×#15692175 | 2 |
| #544×C101 | 2 |
| #3081 | 101 |