Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
440 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 253 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. #20265301 | C2 | direct (N × H) |
| 21. C2×Dic202 | C8 | semidirect |
| 26. C2×#11717579 | Q8 | semidirect |
| 53. Dic202 | C2×C8 | semidirect |
| 56. #11717579 | C2×Q8 | semidirect |
| 68. C2×C101 | C8×Q8 | semidirect |
| 73. C101 | C2×C8×Q8 | semidirect |
| 141. C2 | #20265301 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic202 | 2 |
| #20265301 | 2 |
| C2×#15692184 | 2 |
| C2×C4×#11717579 | 2 |
| C2×C8×Dic101 | 2 |
| C2×C4⋊C8×C101 | 2 |
| C2×C8×Q8 | 101 |