Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. #20266027 | C2 | semidirect |
| 4. Q8⋊#11717581 | C2 | semidirect |
| 30. Q8×D101 | C8 | semidirect |
| 54. Q8×C101 | C2×C8 | semidirect |
| 74. Dic202 | C2×C8 | semidirect |
| 96. D101 | Q8⋊C8 | semidirect |
| 98. C101 | C2×Q8⋊C8 | semidirect |
| 155. Q8 | D101⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊(C4⋊C8) | 2 |
| C4×D101⋊C8 | 2 |
| #20266027 | 2 |
| Q8⋊#11717581 | 2 |
| C4×Q8×D101 | 2 |
| C2×Q8⋊C8 | 101 |