Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#13108058 | C2 | semidirect |
| 3. #20265176 | C2 | direct (N × H) |
| 4. C2×#15692178 | C2 | semidirect |
| 5. C2×#15692175 | C2 | semidirect |
| 6. C22×C4⋊C4×C101 | C2 | semidirect |
| 9. C2×#13108074 | C4 | semidirect |
| 16. C2×#13108058 | C22 | semidirect |
| 18. #15692178 | C22 | semidirect |
| 19. #15692175 | C22 | semidirect |
| 25. C2×C4⋊C4×C101 | C22 | semidirect |
| 29. #13108074 | C2×C4 | semidirect |
| 32. C2×Dic202 | C2×C4 | semidirect |
| 36. C2×D404 | C2×C4 | semidirect |
| 85. D404 | C22×C4 | semidirect |
| 89. Dic202 | C22×C4 | semidirect |
| 110. C2×C101 | #417 | semidirect |
| 116. C101 | C2×#417 | semidirect |
| 119. C22×C4⋊C4 | D101 | semidirect |
| 139. C2×C4⋊C4 | C2×D101 | semidirect |
| 227. C2 | #20265176 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108074 | 2 |
| C22×#13108058 | 2 |
| #20265176 | 2 |
| C2×#15692178 | 2 |
| C2×#15692175 | 2 |
| C22×C4⋊C4×C101 | 2 |
| C2×#417 | 101 |