Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15692274 | C2 | semidirect |
| 3. #20265687 | C2 | semidirect |
| 4. #20265340 | C2 | semidirect |
| 5. #20265335 | C2 | semidirect |
| 6. #20265328 | C2 | semidirect |
| 7. #20265319 | C2 | semidirect |
| 8. #20265315 | C2 | semidirect |
| 9. #20265170 | C2 | semidirect |
| 10. C22⋊C8×D101 | C2 | semidirect |
| 11. #447×C101 | C2 | semidirect |
| 17. C2×#13108073 | C22 | semidirect |
| 23. C2×Dic404 | C22 | semidirect |
| 24. C2×#13108062 | C22 | semidirect |
| 25. C2×#13108062 | C22 | semidirect |
| 26. C2×C8×D101 | C22 | semidirect |
| 28. #15692235 | C22 | semidirect |
| 30. #15692226 | C22 | semidirect |
| 34. #15692213 | C22 | semidirect |
| 35. #15692180 | C22 | semidirect |
| 36. #15692178 | C22 | semidirect |
| 37. #15692176 | C22 | semidirect |
| 39. #15692167 | C22 | semidirect |
| 41. C2×D8×C101 | C22 | semidirect |
| 43. #102×C101 | C22 | semidirect |
| 52. #13108073 | D4 | semidirect |
| 150. C22×C101 | #135 | semidirect |
| 176. C101 | #3002 | semidirect |
| 185. #447 | D101 | semidirect |
| 203. C2×D8 | C2×D101 | semidirect |
| 217. #102 | C2×D101 | semidirect |
| 333. C22 | #15692274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C2×#15692274 | 2 |
| #20265687 | 2 |
| #20265340 | 2 |
| #20265335 | 2 |
| #20265328 | 2 |
| #20265319 | 2 |
| #20265315 | 2 |
| #20265170 | 2 |
| C22⋊C8×D101 | 2 |
| #447×C101 | 2 |
| #3002 | 101 |