Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
368 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 1. C2×#15692314 | C2 | semidirect |
| 2. #20266082 | C2 | direct (N × H) |
| 6. #15692314 | C22 | semidirect |
| 8. C22×D404 | C4 | semidirect |
| 11. #15692252 | C4 | semidirect |
| 13. C2×C42×C101 | C4 | semidirect |
| 28. C2×D404 | C2×C4 | semidirect |
| 34. C42×C101 | C2×C4 | semidirect |
| 80. C2×C101 | #353 | semidirect |
| 86. C101 | C2×#353 | semidirect |
| 97. C2×C42 | #87938 | semidirect |
| 120. C42 | C2×#87938 | semidirect |
| 169. C2 | #20266082 | 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 |
| #20266082 | 2 |
| C2×#15692252 | 2 |
| C2×#353 | 101 |