Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4⋊C4×D433 | C2 | semidirect |
| 3. #28357153 | C2 | semidirect |
| 4. #28357142 | C2 | semidirect |
| 5. #28357140 | C2 | semidirect |
| 6. #28357132 | C2 | semidirect |
| 7. #107×C433 | C2 | semidirect |
| 52. C433 | #480 | semidirect |
| 57. #107 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357195 | 2 |
| C4⋊C4×D433 | 2 |
| #28357153 | 2 |
| #28357142 | 2 |
| #28357140 | 2 |
| #28357132 | 2 |
| #107×C433 | 2 |
| #480 | 433 |