Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1008 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 242 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. C22×#13108084 | C2 | semidirect |
| 2. #20266148 | C2 | direct (N × H) |
| 3. C2×#15692312 | C2 | semidirect |
| 4. C2×C22⋊#11717581 | C2 | semidirect |
| 7. C2×#13108084 | C22 | semidirect |
| 8. C22×#11717581 | C22 | semidirect |
| 9. #15692312 | C22 | semidirect |
| 10. C22⋊#11717581 | C22 | semidirect |
| 23. C2×#11717581 | C23 | semidirect |
| 54. C23×C101 | M16 | semidirect |
| 66. C22×D101 | M16 | semidirect |
| 94. C22×C101 | C2×M16 | semidirect |
| 104. C2×D101 | C2×M16 | semidirect |
| 111. C2×C101 | #407 | semidirect |
| 118. C101 | C2×#407 | semidirect |
| 184. C23 | #13108084 | semidirect |
| 221. C22 | C2×#13108084 | semidirect |
| 231. C2 | #20266148 | 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 |
| #20266148 | 2 |
| C2×#15692312 | 2 |
| C2×C22⋊#11717581 | 2 |
| C23×C4×D101 | 2 |
| C2×#407 | 101 |