Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
644 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 237 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×#15692255 | C2 | semidirect |
| 3. #20265083 | C2 | semidirect |
| 4. #20265075 | C2 | semidirect |
| 5. #20265047 | C2 | semidirect |
| 39. C22×C4×C101 | Q8 | semidirect |
| 77. C22×C101 | C4⋊Q8 | semidirect |
| 86. C4×C101 | C22⋊Q8 | semidirect |
| 96. C101 | #2857 | semidirect |
| 129. C22×C4 | Dic202 | semidirect |
| 173. C22 | #15692255 | semidirect |
| 184. C4 | #15692234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692255 | 2 |
| C2×#15692234 | 2 |
| #20265083 | 2 |
| #20265075 | 2 |
| #20265047 | 2 |
| #20265037 | 2 |
| C22×C42×C101 | 2 |
| #2857 | 101 |