Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#15692263 | C2 | semidirect |
| 3. #20265254 | C2 | semidirect |
| 4. #20265242 | C2 | semidirect |
| 5. #20265145 | C2 | semidirect |
| 6. C2×C4×#11717579 | C2 | semidirect |
| 7. #423×C101 | C2 | semidirect |
| 34. C2×#11717579 | D4 | semidirect |
| 75. C4×C101 | #131 | semidirect |
| 84. C101 | #2931 | semidirect |
| 89. #423 | D101 | semidirect |
| 160. C4 | #15692263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692263 | 2 |
| #20265727 | 2 |
| #20265254 | 2 |
| #20265242 | 2 |
| #20265145 | 2 |
| C2×C4×#11717579 | 2 |
| #423×C101 | 2 |
| #2931 | 101 |