Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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×#15692283 | C2 | semidirect |
| 2. C2×#15692252 | C2 | semidirect |
| 3. C4×#13108074 | C2 | semidirect |
| 4. #20265378 | C2 | semidirect |
| 5. #20265373 | C2 | semidirect |
| 6. #20265183 | C2 | semidirect |
| 7. #423×C101 | C2 | semidirect |
| 12. C2×#13108063 | C22 | semidirect |
| 13. C2×D808 | C22 | semidirect |
| 17. C4×Dic202 | C22 | semidirect |
| 18. C4×D404 | C22 | semidirect |
| 23. #15692177 | C22 | semidirect |
| 26. C4⋊C8×C101 | C22 | semidirect |
| 29. #13108074 | D4 | semidirect |
| 78. D404 | C2×D4 | semidirect |
| 82. Dic202 | C2×D4 | semidirect |
| 94. C4×C101 | AGL(1,ℤ/8) | semidirect |
| 105. C101 | #3038 | semidirect |
| 111. #423 | D101 | semidirect |
| 130. C4⋊C8 | C2×D101 | semidirect |
| 201. C4 | #15692283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692283 | 2 |
| C2×#15692252 | 2 |
| C4×#13108074 | 2 |
| #20265378 | 2 |
| #20265373 | 2 |
| #20265183 | 2 |
| #423×C101 | 2 |
| #3038 | 101 |