Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20265943 | C2 | semidirect |
| 3. #20265159 | C2 | semidirect |
| 4. #20265141 | C2 | semidirect |
| 5. #20264949 | C2 | semidirect |
| 6. #20264948 | C2 | semidirect |
| 7. #407×C101 | C2 | semidirect |
| 42. C2×#11717579 | D4 | semidirect |
| 64. C2×C8×C101 | D4 | semidirect |
| 126. C101 | #1891 | semidirect |
| 131. #407 | D101 | semidirect |
| 184. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265943 | 2 |
| #20265688 | 2 |
| #20265159 | 2 |
| #20265141 | 2 |
| #20264949 | 2 |
| #20264948 | 2 |
| #407×C101 | 2 |
| #1891 | 101 |