Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#15692274 | C2 | semidirect |
| 2. #20265847 | C2 | semidirect |
| 3. #20265410 | C2 | semidirect |
| 4. #20265374 | C2 | semidirect |
| 5. #20265319 | C2 | semidirect |
| 6. C4×Dic404 | C2 | semidirect |
| 7. C8×D404 | C2 | semidirect |
| 8. #493×C101 | C2 | semidirect |
| 37. Dic404 | D4 | semidirect |
| 86. C4×C101 | #135 | semidirect |
| 98. C101 | #3287 | semidirect |
| 101. #493 | D101 | semidirect |
| 187. C4 | #15692274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692274 | 2 |
| #20265847 | 2 |
| #20265410 | 2 |
| #20265374 | 2 |
| #20265319 | 2 |
| C4×Dic404 | 2 |
| C8×D404 | 2 |
| #493×C101 | 2 |
| #3287 | 101 |