Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13108073 | C2 | semidirect |
| 2. C22×#13108062 | C2 | semidirect |
| 3. C2×#15692226 | C2 | semidirect |
| 4. #20265319 | C2 | direct (N × H) |
| 5. C2×#15692180 | C2 | semidirect |
| 6. C2×#15692176 | C2 | semidirect |
| 7. C2×#15692167 | C2 | semidirect |
| 8. C22×D8×C101 | C2 | semidirect |
| 12. C2×#13108073 | C22 | semidirect |
| 19. C2×#13108062 | C22 | semidirect |
| 22. #15692226 | C22 | semidirect |
| 25. #15692180 | C22 | semidirect |
| 26. #15692176 | C22 | semidirect |
| 27. #15692167 | C22 | semidirect |
| 31. C2×D8×C101 | C22 | semidirect |
| 39. C2×Dic202 | D4 | semidirect |
| 67. C2×D4×C101 | D4 | semidirect |
| 92. D4×C101 | C2×D4 | semidirect |
| 111. Dic202 | C2×D4 | semidirect |
| 138. C2×C101 | #449 | semidirect |
| 144. C101 | C2×#449 | semidirect |
| 147. C22×D8 | D101 | semidirect |
| 167. C2×D8 | C2×D101 | semidirect |
| 196. C2×D4 | C22⋊D101 | semidirect |
| 241. D4 | C2×C22⋊D101 | semidirect |
| 283. C2 | #20265319 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C22×#13108062 | 2 |
| C2×#15692226 | 2 |
| #20265319 | 2 |
| C2×#15692180 | 2 |
| C2×#15692176 | 2 |
| C2×#15692167 | 2 |
| C22×D8×C101 | 2 |
| C2×#449 | 101 |