Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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×#16812367 | C2 | semidirect |
| 2. C22⋊#16812367 | C2 | direct (N × H) |
| 5. C2×#16812367 | C22 | semidirect |
| 22. C22×D433 | C8 | semidirect |
| 23. C22×D433 | C8 | semidirect |
| 26. C23×C433 | C8 | semidirect |
| 29. C22×C433 | C2×C8 | semidirect |
| 36. C2×D433 | C2×C8 | semidirect |
| 43. C2×C433 | C22⋊C8 | semidirect |
| 46. D433 | C22⋊C8 | semidirect |
| 49. C433 | C2×C22⋊C8 | semidirect |
| 68. C23 | #16812367 | semidirect |
| 88. C22 | C2×#16812367 | semidirect |
| 97. C2 | C22⋊#16812367 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16812367 | 2 |
| C22⋊#16812367 | 2 |
| C23×#13181884 | 2 |
| C2×C22⋊C8 | 433 |