Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 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×#20294080 | C2 | semidirect |
| 3. C22⋊#16812358 | C2 | semidirect |
| 4. #28357132 | C2 | semidirect |
| 5. C22⋊C8×C433 | C2 | semidirect |
| 14. C2×#16812358 | C22 | semidirect |
| 16. C2×C8×C433 | C22 | semidirect |
| 37. C22×C433 | M16 | semidirect |
| 45. C2×D433 | M16 | semidirect |
| 56. C433 | #407 | semidirect |
| 62. C22⋊C8 | D433 | semidirect |
| 73. C2×C8 | C2×D433 | semidirect |
| 101. C22 | #20294080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D433 | 2 |
| C2×#20294080 | 2 |
| C22⋊#16812358 | 2 |
| #28357132 | 2 |
| C22⋊C8×C433 | 2 |
| #407 | 433 |