Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20265789 | C2 | semidirect |
| 3. #20265519 | C2 | semidirect |
| 4. #20265478 | C2 | semidirect |
| 5. #20265383 | C2 | semidirect |
| 7. #20265279 | C2 | semidirect |
| 8. C4×#13108063 | C2 | semidirect |
| 9. #433×C101 | C2 | semidirect |
| 13. #15692255 | C22 | semidirect |
| 15. #15692247 | C22 | semidirect |
| 18. C4×Dic202 | C22 | semidirect |
| 24. #15692189 | C22 | semidirect |
| 25. #15692187 | C22 | semidirect |
| 26. #15692180 | C22 | semidirect |
| 27. #15692180 | C22 | semidirect |
| 31. C4⋊C8×C101 | C22 | semidirect |
| 33. #97×C101 | C22 | semidirect |
| 34. C4×C8×C101 | C22 | semidirect |
| 103. C101 | #3123 | semidirect |
| 112. #433 | D101 | semidirect |
| 130. C4⋊C8 | C2×D101 | semidirect |
| 136. #97 | C2×D101 | semidirect |
| 137. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265789 | 2 |
| #20265651 | 2 |
| #20265519 | 2 |
| #20265478 | 2 |
| #20265383 | 2 |
| #20265330 | 2 |
| #20265279 | 2 |
| C4×#13108063 | 2 |
| #433×C101 | 2 |
| #3123 | 101 |