Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20265543 | C2 | semidirect |
| 3. #20265539 | C2 | semidirect |
| 4. #20265534 | C2 | semidirect |
| 5. #20265525 | C2 | semidirect |
| 6. #20265181 | C2 | semidirect |
| 7. #20265176 | C2 | semidirect |
| 8. #20265171 | C2 | semidirect |
| 9. C2×#15692175 | C2 | semidirect |
| 10. #20265133 | C2 | semidirect |
| 11. #544×C101 | C2 | semidirect |
| 21. #15692178 | C22 | semidirect |
| 22. #15692178 | C22 | semidirect |
| 23. #15692178 | C22 | semidirect |
| 28. #15692175 | C22 | semidirect |
| 29. #15692175 | C22 | semidirect |
| 30. #15692175 | C22 | semidirect |
| 31. #15692166 | C22 | semidirect |
| 32. C4×#11717579 | C22 | semidirect |
| 34. C4⋊Q8×C101 | C22 | semidirect |
| 36. #125×C101 | C22 | semidirect |
| 136. C101 | #3136 | semidirect |
| 137. #544 | D101 | semidirect |
| 153. C4⋊Q8 | C2×D101 | semidirect |
| 156. #125 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265746 | 2 |
| #20265543 | 2 |
| #20265539 | 2 |
| #20265534 | 2 |
| #20265525 | 2 |
| #20265181 | 2 |
| #20265176 | 2 |
| #20265171 | 2 |
| C2×#15692175 | 2 |
| #20265133 | 2 |
| #544×C101 | 2 |
| #3136 | 101 |