Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20265657 | C2 | semidirect |
| 3. #20265279 | C2 | semidirect |
| 4. C4×Dic404 | C2 | semidirect |
| 5. C4×D808 | C2 | semidirect |
| 6. C2×#15692189 | C2 | semidirect |
| 7. #20265179 | C2 | semidirect |
| 8. #405×C101 | C2 | semidirect |
| 10. #15692277 | C4 | semidirect |
| 30. #13108074 | C2×C4 | semidirect |
| 37. Dic404 | C2×C4 | semidirect |
| 38. #13108063 | C2×C4 | semidirect |
| 39. D808 | C2×C4 | semidirect |
| 47. C2×C8×C101 | C2×C4 | semidirect |
| 96. C101 | #2951 | semidirect |
| 104. #405 | D101 | semidirect |
| 138. C2×C8 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| #20265657 | 2 |
| #20265279 | 2 |
| C4×Dic404 | 2 |
| C4×D808 | 2 |
| C2×#15692189 | 2 |
| #20265179 | 2 |
| #405×C101 | 2 |
| #2951 | 101 |