Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
192 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 71 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. D4×#11717579 | C2 | semidirect |
| 3. #20265242 | C2 | semidirect |
| 4. #20264927 | C2 | semidirect |
| 5. #20264906 | C2 | semidirect |
| 6. #20264899 | C2 | semidirect |
| 7. D4⋊C8×C101 | C2 | semidirect |
| 25. #13108059 | C8 | semidirect |
| 45. D4×C101 | C2×C8 | semidirect |
| 54. D404 | C2×C8 | semidirect |
| 63. #11717579 | C2×C8 | semidirect |
| 84. C101 | #1580 | semidirect |
| 90. D4⋊C8 | D101 | semidirect |
| 131. D4 | C8×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13108059 | 2 |
| D4×#11717579 | 2 |
| #20265242 | 2 |
| #20264927 | 2 |
| #20264906 | 2 |
| #20264899 | 2 |
| D4⋊C8×C101 | 2 |
| #1580 | 101 |