Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
124 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 124 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 |
|---|---|---|
| 1. C2×#20294081 | C2 | semidirect |
| 2. C22×#16812358 | C2 | semidirect |
| 3. C4⋊#16812358 | C2 | semidirect |
| 4. C22⋊#16812358 | C2 | semidirect |
| 5. C22⋊#16812358 | C2 | semidirect |
| 6. #28357131 | C2 | semidirect |
| 24. #16812358 | D4 | semidirect |
| 42. C22×C433 | M16 | semidirect |
| 55. C433 | #435 | semidirect |
| 98. C22 | #20294081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294081 | 2 |
| C22×#16812358 | 2 |
| C4⋊#16812358 | 2 |
| C22⋊#16812358 | 2 |
| #28357131 | 2 |
| C4×D4×C433 | 2 |
| #435 | 433 |