Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20265654 | C2 | semidirect |
| 4. #20265279 | C2 | semidirect |
| 5. C4×#13108063 | C2 | semidirect |
| 6. #20265215 | C2 | semidirect |
| 7. #20265187 | C2 | semidirect |
| 9. #405×C101 | C2 | semidirect |
| 12. C2×#13108063 | C4 | semidirect |
| 15. C4×Dic202 | C22 | semidirect |
| 23. #15692189 | C22 | semidirect |
| 24. #15692187 | C22 | semidirect |
| 25. #15692180 | C22 | semidirect |
| 30. #97×C101 | C22 | semidirect |
| 31. C4×C8×C101 | C22 | semidirect |
| 35. C2×Dic202 | C2×C4 | semidirect |
| 43. #13108063 | C2×C4 | semidirect |
| 44. #13108063 | C2×C4 | semidirect |
| 56. C2×C8×C101 | C2×C4 | semidirect |
| 104. C101 | #2949 | semidirect |
| 113. #405 | D101 | semidirect |
| 134. #97 | C2×D101 | semidirect |
| 135. C4×C8 | C2×D101 | semidirect |
| 151. C2×C8 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108063 | 2 |
| #20265654 | 2 |
| #20265651 | 2 |
| #20265279 | 2 |
| C4×#13108063 | 2 |
| #20265215 | 2 |
| #20265187 | 2 |
| #20265183 | 2 |
| #405×C101 | 2 |
| #2949 | 101 |