Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
576 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 250 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. #20266181 | C2 | direct (N × H) |
| 3. C2×C4⋊#11717581 | C2 | semidirect |
| 8. C4⋊#11717581 | C22 | semidirect |
| 39. C2×C4×C101 | M16 | semidirect |
| 60. C4×C101 | C2×M16 | semidirect |
| 65. C2×C101 | #423 | semidirect |
| 70. C101 | C2×#423 | semidirect |
| 119. C2×C4 | #13108084 | semidirect |
| 134. C4 | C2×#13108084 | semidirect |
| 136. C2 | #20266181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108084 | 2 |
| #20266181 | 2 |
| C2×C4⋊#11717581 | 2 |
| C2×C42×D101 | 2 |
| C2×#423 | 101 |