Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
336 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 44. Q8×C101 | Q16 | semidirect |
| 70. C101 | #3363 | semidirect |
| 117. Q8 | #13108064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic202 | 2 |
| #20265527 | 2 |
| #20265472 | 2 |
| #20265384 | 2 |
| Q8×#11717579 | 2 |
| C4×#13108064 | 2 |
| #557×C101 | 2 |
| #3363 | 101 |