Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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. #20266188 | C2 | semidirect |
| 3. #20266187 | C2 | semidirect |
| 4. C2×#15692324 | C2 | semidirect |
| 15. #15692263 | C4 | semidirect |
| 16. #15692262 | C4 | semidirect |
| 17. #15692261 | C4 | semidirect |
| 20. #131×C101 | C4 | semidirect |
| 33. #13108058 | C2×C4 | semidirect |
| 34. #13108057 | C2×C4 | semidirect |
| 35. C2×#11717579 | C2×C4 | semidirect |
| 36. C8×D101 | C2×C4 | semidirect |
| 37. C8×D101 | C2×C4 | semidirect |
| 41. M16×C101 | C2×C4 | semidirect |
| 42. C2×C8×C101 | C2×C4 | semidirect |
| 79. C101 | #2913 | semidirect |
| 89. #131 | #87938 | semidirect |
| 110. M16 | C2×#87938 | semidirect |
| 116. C2×C8 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266246 | 2 |
| #20266188 | 2 |
| #20266187 | 2 |
| C2×#15692324 | 2 |
| #131×D101 | 2 |
| #2913 | 101 |