Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
440 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 234 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. #20266226 | C2 | direct (N × H) |
| 23. C2×#11717581 | Q8 | semidirect |
| 27. C2×Dic202 | C8 | semidirect |
| 53. Dic202 | C2×C8 | semidirect |
| 56. #11717581 | C2×Q8 | semidirect |
| 68. C2×C101 | C8×Q8 | semidirect |
| 73. C101 | C2×C8×Q8 | semidirect |
| 141. C2 | #20266226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266226 | 2 |
| C2×#15692322 | 2 |
| C2×C4⋊#11717581 | 2 |
| C2×C4×#11717581 | 2 |
| C2×#15692220 | 2 |
| C2×C8×Q8 | 101 |