Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15692282 | C2 | semidirect |
| 2. #20265728 | C2 | semidirect |
| 3. C4×D4×D101 | C2 | semidirect |
| 4. #20265395 | C2 | semidirect |
| 5. #20265394 | C2 | semidirect |
| 6. #20265379 | C2 | semidirect |
| 7. #20265373 | C2 | semidirect |
| 8. #20265372 | C2 | semidirect |
| 9. #20265199 | C2 | semidirect |
| 10. #20265177 | C2 | semidirect |
| 11. #461×C101 | C2 | semidirect |
| 20. #15692252 | C22 | semidirect |
| 21. #15692244 | C22 | semidirect |
| 34. C4⋊#11717579 | C22 | semidirect |
| 35. #15692184 | C22 | semidirect |
| 36. #15692179 | C22 | semidirect |
| 37. #15692177 | C22 | semidirect |
| 38. #15692175 | C22 | semidirect |
| 40. C4⋊Q8×C101 | C22 | semidirect |
| 42. C4⋊C8×C101 | C22 | semidirect |
| 43. #103×C101 | C22 | semidirect |
| 54. D4×D101 | D4 | semidirect |
| 146. C4×C101 | AGL(1,ℤ/8) | semidirect |
| 161. C101 | #3036 | semidirect |
| 168. #461 | D101 | semidirect |
| 182. C4⋊Q8 | C2×D101 | semidirect |
| 200. C4⋊C8 | C2×D101 | semidirect |
| 202. #103 | C2×D101 | semidirect |
| 311. C4 | #15692282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692282 | 2 |
| #20265728 | 2 |
| C4×D4×D101 | 2 |
| #20265395 | 2 |
| #20265394 | 2 |
| #20265379 | 2 |
| #20265373 | 2 |
| #20265372 | 2 |
| #20265199 | 2 |
| #20265177 | 2 |
| #461×C101 | 2 |
| #3036 | 101 |