Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#13108063 | C2 | semidirect |
| 3. #20265753 | C2 | semidirect |
| 4. #20265651 | C2 | semidirect |
| 5. #20265393 | C2 | semidirect |
| 6. #20265383 | C2 | semidirect |
| 7. #20265187 | C2 | semidirect |
| 8. #20265174 | C2 | semidirect |
| 9. #424×C101 | C2 | semidirect |
| 18. #15692255 | C22 | semidirect |
| 19. #15692243 | C22 | semidirect |
| 26. #15692180 | C22 | semidirect |
| 27. #15692180 | C22 | semidirect |
| 28. #15692177 | C22 | semidirect |
| 32. C4⋊C8×C101 | C22 | semidirect |
| 117. C101 | #3042 | semidirect |
| 124. #424 | D101 | semidirect |
| 146. C4⋊C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692283 | 2 |
| C22×#13108063 | 2 |
| #20265753 | 2 |
| #20265651 | 2 |
| #20265393 | 2 |
| #20265383 | 2 |
| #20265187 | 2 |
| #20265174 | 2 |
| #424×C101 | 2 |
| #3042 | 101 |