Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20265254 | C2 | semidirect |
| 3. D4×#11717579 | C2 | semidirect |
| 4. #20264927 | C2 | semidirect |
| 5. #20264906 | C2 | semidirect |
| 6. #20264898 | C2 | semidirect |
| 7. D4⋊C8×C101 | C2 | semidirect |
| 45. D4×C101 | M16 | semidirect |
| 84. C101 | #1586 | semidirect |
| 90. D4⋊C8 | D101 | semidirect |
| 131. D4 | #13108057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13108059 | 2 |
| #20265254 | 2 |
| D4×#11717579 | 2 |
| #20264927 | 2 |
| #20264906 | 2 |
| #20264898 | 2 |
| D4⋊C8×C101 | 2 |
| #1586 | 101 |