Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 3. #20265097 | C2 | direct (N × H) |
| 29. C22×Dic101 | Q8 | semidirect |
| 40. C22×C4×C101 | Q8 | semidirect |
| 60. C2×C4×C101 | C2×Q8 | semidirect |
| 68. C2×Dic101 | C2×Q8 | semidirect |
| 85. C2×C101 | #395 | semidirect |
| 92. C101 | C2×#395 | semidirect |
| 130. C22×C4 | Dic202 | semidirect |
| 161. C2×C4 | C2×Dic202 | semidirect |
| 177. C2 | #20265097 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic202 | 2 |
| C22×#13108053 | 2 |
| #20265097 | 2 |
| C2×#15692162 | 2 |
| C22×C4⋊C4×C101 | 2 |
| C2×#395 | 101 |