Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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×#20294107 | C2 | semidirect |
| 2. C22×#16812365 | C2 | semidirect |
| 3. C4⋊#16812365 | C2 | semidirect |
| 4. #28357277 | C2 | semidirect |
| 5. C22⋊#16812365 | C2 | semidirect |
| 6. #28357275 | C2 | semidirect |
| 24. #16812365 | D4 | semidirect |
| 39. C22×C433 | M16 | semidirect |
| 55. C433 | #435 | semidirect |
| 98. C22 | #20294107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294107 | 2 |
| C22×#16812365 | 2 |
| C4⋊#16812365 | 2 |
| #28357277 | 2 |
| C22⋊#16812365 | 2 |
| #28357275 | 2 |
| #28357180 | 2 |
| #435 | 433 |