Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692281 | C2 | semidirect |
| 3. C2×#15692251 | C2 | semidirect |
| 4. #20265645 | C2 | semidirect |
| 5. #20265376 | C2 | semidirect |
| 6. #20265371 | C2 | semidirect |
| 7. #20265200 | C2 | semidirect |
| 8. #20265181 | C2 | semidirect |
| 9. #418×C101 | C2 | semidirect |
| 15. C2×#13108063 | C22 | semidirect |
| 16. C2×#13108062 | C22 | semidirect |
| 17. C2×D808 | C22 | semidirect |
| 18. C2×#13108059 | C22 | semidirect |
| 23. #15692220 | C22 | semidirect |
| 24. #15692217 | C22 | semidirect |
| 29. #15692184 | C22 | semidirect |
| 30. #15692175 | C22 | semidirect |
| 34. #102×C101 | C22 | semidirect |
| 37. #13108074 | D4 | semidirect |
| 101. D404 | C2×D4 | semidirect |
| 105. Dic202 | C2×D4 | semidirect |
| 125. Dic101 | AGL(1,ℤ/8) | semidirect |
| 133. C101 | #3038 | semidirect |
| 142. #418 | D101 | semidirect |
| 167. #102 | 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 |
| C2×#15692281 | 2 |
| C2×#15692251 | 2 |
| #20265645 | 2 |
| #20265376 | 2 |
| #20265371 | 2 |
| #20265200 | 2 |
| #20265181 | 2 |
| #418×C101 | 2 |
| #3038 | 101 |