Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#15692286 | C2 | semidirect |
| 3. #20265359 | C2 | semidirect |
| 4. #20265354 | C2 | semidirect |
| 5. #20265195 | C2 | semidirect |
| 6. #20265161 | C2 | semidirect |
| 7. #536×C101 | C2 | semidirect |
| 17. #15692286 | C22 | semidirect |
| 20. C2×#13108058 | C22 | semidirect |
| 21. #15692183 | C22 | semidirect |
| 22. #15692174 | C22 | semidirect |
| 23. #15692172 | C22 | semidirect |
| 25. C22×Q8×C101 | C22 | semidirect |
| 26. C4⋊Q8×C101 | C22 | semidirect |
| 27. #124×C101 | C22 | semidirect |
| 30. #117×C101 | C22 | semidirect |
| 130. C101 | #3022 | semidirect |
| 133. #536 | D101 | semidirect |
| 147. C22×Q8 | C2×D101 | semidirect |
| 153. C4⋊Q8 | C2×D101 | semidirect |
| 154. #124 | C2×D101 | semidirect |
| 157. #117 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266013 | 2 |
| C2×#15692286 | 2 |
| #20265359 | 2 |
| #20265354 | 2 |
| #20265195 | 2 |
| #20265161 | 2 |
| #536×C101 | 2 |
| #3022 | 101 |