Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×D404 | C2 | semidirect |
| 3. C2×#15692176 | C2 | semidirect |
| 4. C2×#15692175 | C2 | semidirect |
| 5. #20264939 | C2 | semidirect |
| 6. #20264932 | C2 | semidirect |
| 7. #390×C101 | C2 | semidirect |
| 12. C2×#13108059 | C4 | semidirect |
| 43. C2×#11717579 | C2×C4 | semidirect |
| 53. C2×D4×C101 | C2×C4 | semidirect |
| 91. C2×C4×C101 | D8 | semidirect |
| 104. D404 | C22⋊C4 | semidirect |
| 147. C101 | #1879 | semidirect |
| 152. #390 | D101 | semidirect |
| 186. C2×D4 | C4×D101 | semidirect |
| 246. C2×C4 | #13108059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108059 | 2 |
| C2×C4×D404 | 2 |
| C2×#15692176 | 2 |
| C2×#15692175 | 2 |
| #20264939 | 2 |
| #20264932 | 2 |
| #390×C101 | 2 |
| #1879 | 101 |