Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20265217 | C2 | semidirect |
| 4. #20265046 | C2 | semidirect |
| 5. #20264945 | C2 | semidirect |
| 6. #20264938 | C2 | semidirect |
| 20. #15692182 | C4 | semidirect |
| 30. #13108058 | C2×C4 | semidirect |
| 43. C4×Dic101 | C2×C4 | semidirect |
| 62. Q8×C101 | C4⋊C4 | semidirect |
| 66. D4×C101 | C4⋊C4 | semidirect |
| 113. C101 | #1859 | semidirect |
| 175. Q8 | #13108053 | semidirect |
| 179. D4 | #13108053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265660 | 2 |
| #20265217 | 2 |
| C2×#15692182 | 2 |
| #20265046 | 2 |
| #20264945 | 2 |
| #20264938 | 2 |
| #417×C101 | 2 |
| #1859 | 101 |