Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 16. #15692165 | C4 | semidirect |
| 63. C8×C101 | C4⋊C4 | semidirect |
| 64. #11717579 | C4⋊C4 | semidirect |
| 85. C101 | #1847 | semidirect |
| 149. C8 | #13108053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692189 | 2 |
| C2×#15692188 | 2 |
| C2×#15692186 | 2 |
| C2×#15692165 | 2 |
| #20265046 | 2 |
| #20265042 | 2 |
| C2×#106×C101 | 2 |
| #1847 | 101 |