Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D433 | C2 | semidirect |
| 2. C2×#20294086 | C2 | semidirect |
| 3. C2×#20294084 | C2 | semidirect |
| 5. #28357143 | C2 | semidirect |
| 6. #28357132 | C2 | semidirect |
| 7. #103×C433 | C2 | semidirect |
| 27. Dic866 | D4 | semidirect |
| 38. Q8×C433 | D4 | semidirect |
| 49. C2×D433 | SD16 | semidirect |
| 61. C433 | #448 | semidirect |
| 68. #103 | D433 | semidirect |
| 91. Q8 | D1732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D433 | 2 |
| C2×#20294086 | 2 |
| C2×#20294084 | 2 |
| #28357195 | 2 |
| #28357143 | 2 |
| #28357132 | 2 |
| #103×C433 | 2 |
| #448 | 433 |