Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
296 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 9. #15692322 | C4 | semidirect |
| 11. C4×#11717581 | C4 | semidirect |
| 29. #13108053 | C8 | semidirect |
| 55. #11717581 | C4⋊C4 | semidirect |
| 64. Dic101 | C4×C8 | semidirect |
| 75. C101 | C8×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692322 | 2 |
| C2×C4×#11717581 | 2 |
| #20266043 | 2 |
| #20265028 | 2 |
| C8×C4⋊C4 | 101 |