Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
436 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 166 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. C2×C4×#11717581 | C2 | semidirect |
| 3. #20266043 | C2 | semidirect |
| 6. C22⋊#11717581 | C4 | direct (N × H) |
| 18. C2×#11717581 | C2×C4 | semidirect |
| 23. C22×Dic101 | C8 | semidirect |
| 36. C22×C4×C101 | C8 | semidirect |
| 75. C22×C101 | C4×C8 | semidirect |
| 84. C4×C101 | C22⋊C8 | semidirect |
| 87. Dic101 | C22⋊C8 | semidirect |
| 98. C101 | C4×C22⋊C8 | semidirect |
| 127. C22×C4 | #11717581 | semidirect |
| 173. C22 | C4×#11717581 | semidirect |
| 186. C4 | C22⋊#11717581 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11717581 | 2 |
| C2×C4×#11717581 | 2 |
| #20266043 | 2 |
| C22×C4×Dic101 | 2 |
| C4×C22⋊C8 | 101 |