Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692300 | C2 | semidirect |
| 2. C2×#15692281 | C2 | semidirect |
| 3. #20265744 | C2 | semidirect |
| 4. #20265319 | C2 | semidirect |
| 5. #20265309 | C2 | semidirect |
| 6. #20265182 | C2 | semidirect |
| 7. #20265174 | C2 | semidirect |
| 8. #20265143 | C2 | semidirect |
| 9. C22×D8×C101 | C2 | semidirect |
| 15. C2×#13108073 | C22 | semidirect |
| 18. C2×D4×D101 | C22 | semidirect |
| 20. C2×#13108062 | C22 | semidirect |
| 21. C2×#13108059 | C22 | semidirect |
| 22. C2×#13108058 | C22 | semidirect |
| 25. #15692226 | C22 | semidirect |
| 27. #15692214 | C22 | semidirect |
| 28. #15692180 | C22 | semidirect |
| 29. #15692177 | C22 | semidirect |
| 30. #15692176 | C22 | semidirect |
| 31. #15692167 | C22 | semidirect |
| 33. C22×D4×C101 | C22 | semidirect |
| 35. C2×D8×C101 | C22 | semidirect |
| 36. C22×C8×C101 | C22 | semidirect |
| 41. #13108074 | D4 | semidirect |
| 76. C2×D4×C101 | D4 | semidirect |
| 152. C101 | #3008 | semidirect |
| 155. C22×D8 | D101 | semidirect |
| 172. C22×D4 | C2×D101 | semidirect |
| 177. C2×D8 | C2×D101 | semidirect |
| 179. C22×C8 | C2×D101 | semidirect |
| 217. C2×D4 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692300 | 2 |
| C2×#15692281 | 2 |
| #20265744 | 2 |
| #20265319 | 2 |
| #20265309 | 2 |
| #20265182 | 2 |
| #20265174 | 2 |
| #20265143 | 2 |
| C22×D8×C101 | 2 |
| #3008 | 101 |