Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 1. C2×#15692286 | C2 | semidirect |
| 3. #20265655 | C2 | semidirect |
| 4. #20265397 | C2 | semidirect |
| 5. #20265375 | C2 | semidirect |
| 6. #20265203 | C2 | semidirect |
| 7. #20265182 | C2 | semidirect |
| 8. #20265174 | C2 | semidirect |
| 9. C22×SD16×C101 | C2 | semidirect |
| 12. C2×#13108064 | C22 | semidirect |
| 13. C2×#13108061 | C22 | semidirect |
| 20. Q8×Dic101 | C22 | semidirect |
| 24. #15692184 | C22 | semidirect |
| 25. #15692180 | C22 | semidirect |
| 26. #15692177 | C22 | semidirect |
| 56. C2×Q8×C101 | D4 | semidirect |
| 117. C101 | #3043 | semidirect |
| 119. C22×SD16 | D101 | semidirect |
| 156. C2×Q8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692286 | 2 |
| #20265744 | 2 |
| #20265655 | 2 |
| #20265397 | 2 |
| #20265375 | 2 |
| #20265203 | 2 |
| #20265182 | 2 |
| #20265174 | 2 |
| C22×SD16×C101 | 2 |
| #3043 | 101 |