Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×#15692220 | C2 | semidirect |
| 4. #20265274 | C2 | direct (N × H) |
| 5. C2×#15692188 | C2 | semidirect |
| 6. C2×#15692180 | C2 | semidirect |
| 7. C2×#15692165 | C2 | semidirect |
| 11. C2×#13108062 | C4 | semidirect |
| 15. #15692220 | C22 | semidirect |
| 23. #15692188 | C22 | semidirect |
| 24. #15692180 | C22 | semidirect |
| 25. #15692165 | C22 | semidirect |
| 32. C2×Dic202 | C2×C4 | semidirect |
| 40. #13108062 | C2×C4 | semidirect |
| 41. C2×#11717579 | C2×C4 | semidirect |
| 86. Dic202 | C22×C4 | semidirect |
| 88. #11717579 | C22×C4 | semidirect |
| 106. C2×C101 | #440 | semidirect |
| 111. C101 | C2×#440 | semidirect |
| 217. C2 | #20265274 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| C2×#15692220 | 2 |
| C2×D4×Dic101 | 2 |
| #20265274 | 2 |
| C2×#15692188 | 2 |
| C2×#15692180 | 2 |
| C2×#15692165 | 2 |
| C2×#102×C101 | 2 |
| C2×#440 | 101 |