Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 1. D4×Dic202 | C2 | semidirect |
| 3. #20265528 | C2 | semidirect |
| 4. #20265508 | C2 | semidirect |
| 5. #20265463 | C2 | semidirect |
| 6. #20265406 | C2 | semidirect |
| 7. #20265383 | C2 | semidirect |
| 8. #20265318 | C2 | semidirect |
| 9. C4×#13108063 | C2 | semidirect |
| 10. C2×#15692180 | C2 | semidirect |
| 11. C8×D4×C101 | C2 | semidirect |
| 79. D4×C101 | SD16 | semidirect |
| 102. Dic202 | #41 | semidirect |
| 129. C101 | #3298 | semidirect |
| 139. C8×D4 | D101 | semidirect |
| 217. D4 | #13108063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic202 | 2 |
| #20265831 | 2 |
| #20265528 | 2 |
| #20265508 | 2 |
| #20265463 | 2 |
| #20265406 | 2 |
| #20265383 | 2 |
| #20265318 | 2 |
| C4×#13108063 | 2 |
| C2×#15692180 | 2 |
| C8×D4×C101 | 2 |
| #3298 | 101 |