Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#15692286 | C2 | semidirect |
| 2. C22×#13108061 | C2 | semidirect |
| 4. #20265399 | C2 | semidirect |
| 5. #20265377 | C2 | semidirect |
| 6. #20265204 | C2 | semidirect |
| 7. #20265181 | C2 | semidirect |
| 8. #20265171 | C2 | semidirect |
| 9. #519×C101 | C2 | semidirect |
| 13. C2×#13108064 | C22 | semidirect |
| 16. C2×#13108061 | C22 | semidirect |
| 23. C4⋊#11717579 | C22 | semidirect |
| 24. #15692178 | C22 | semidirect |
| 26. #15692175 | C22 | semidirect |
| 29. C4×Q8×C101 | C22 | semidirect |
| 55. C2×Q8×C101 | D4 | semidirect |
| 117. C101 | #3043 | semidirect |
| 121. #519 | D101 | semidirect |
| 142. C4×Q8 | C2×D101 | semidirect |
| 156. C2×Q8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692286 | 2 |
| C22×#13108061 | 2 |
| #20265746 | 2 |
| #20265399 | 2 |
| #20265377 | 2 |
| #20265204 | 2 |
| #20265181 | 2 |
| #20265171 | 2 |
| #519×C101 | 2 |
| #3043 | 101 |