Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692246 | C2 | semidirect |
| 3. #20265530 | C2 | direct (N × H) |
| 4. C2×#15692180 | C2 | semidirect |
| 5. C2×#15692178 | C2 | semidirect |
| 7. C2×C8×Dic101 | C2 | semidirect |
| 12. #15692246 | C22 | semidirect |
| 21. #15692180 | C22 | semidirect |
| 22. #15692178 | C22 | semidirect |
| 24. C8×Dic101 | C22 | semidirect |
| 102. C2×C101 | #488 | semidirect |
| 107. C101 | C2×#488 | semidirect |
| 209. C2 | #20265530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692246 | 2 |
| C2×#15692242 | 2 |
| #20265530 | 2 |
| C2×#15692180 | 2 |
| C2×#15692178 | 2 |
| C2×#15692176 | 2 |
| C2×C8×Dic101 | 2 |
| C2×#102×C101 | 2 |
| C2×#488 | 101 |