Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20265580 | C2 | semidirect |
| 3. #20265556 | C2 | semidirect |
| 4. #20265529 | C2 | semidirect |
| 5. #20265527 | C2 | semidirect |
| 7. C4×#13108064 | C2 | semidirect |
| 73. C2×C4×C101 | Q16 | semidirect |
| 105. C101 | #3170 | semidirect |
| 182. C2×C4 | #13108064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265734 | 2 |
| #20265580 | 2 |
| #20265556 | 2 |
| #20265529 | 2 |
| #20265527 | 2 |
| #20265416 | 2 |
| C4×#13108064 | 2 |
| C2×C4×#11717579 | 2 |
| #533×C101 | 2 |
| #3170 | 101 |