Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
182 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20265255 | C2 | semidirect |
| 2. D4×#11717579 | C2 | semidirect |
| 3. #20264930 | C2 | semidirect |
| 4. D4⋊#11717579 | C2 | semidirect |
| 5. D4⋊#11717579 | C2 | semidirect |
| 6. #20264899 | C2 | semidirect |
| 47. D4×C101 | M16 | semidirect |
| 63. #11717579 | D8 | semidirect |
| 84. C101 | #1581 | semidirect |
| 131. D4 | #13108058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265255 | 2 |
| D4×#11717579 | 2 |
| #20264930 | 2 |
| D4⋊#11717579 | 2 |
| #20264899 | 2 |
| C4×D8×C101 | 2 |
| #1581 | 101 |