Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20266084 | C2 | direct (N × H) |
| 7. C22×Dic202 | C4 | semidirect |
| 10. #15692243 | C4 | semidirect |
| 13. C2×C42×C101 | C4 | semidirect |
| 21. C2×Dic202 | C2×C4 | semidirect |
| 33. C42×C101 | C2×C4 | semidirect |
| 73. C2×C101 | #354 | semidirect |
| 78. C101 | C2×#354 | semidirect |
| 89. C2×C42 | #87938 | semidirect |
| 111. C42 | C2×#87938 | semidirect |
| 153. C2 | #20266084 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692314 | 2 |
| #20266084 | 2 |
| C2×#15692243 | 2 |
| C2×#354 | 101 |