Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C4⋊Dic433 | C2 | semidirect |
| 3. #28357144 | C2 | semidirect |
| 4. #28357141 | C2 | semidirect |
| 12. #41×C433 | C4 | semidirect |
| 24. Q8×C433 | C2×C4 | semidirect |
| 27. D4×C433 | C2×C4 | semidirect |
| 51. C433 | #417 | semidirect |
| 59. #41 | Dic433 | semidirect |
| 73. Q8 | C2×Dic433 | semidirect |
| 76. D4 | C2×Dic433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294081 | 2 |
| C2×C4⋊Dic433 | 2 |
| #28357144 | 2 |
| #28357141 | 2 |
| C2×#41×C433 | 2 |
| #417 | 433 |