Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 67 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. C8×Dic422 | C2 | semidirect |
| 3. #27212896 | C2 | semidirect |
| 4. #27212876 | C2 | semidirect |
| 6. #27212867 | C2 | semidirect |
| 42. Dic422 | M16 | semidirect |
| 60. C8×C211 | SD16 | semidirect |
| 77. C211 | #1583 | semidirect |
| 138. C8 | #16809950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic422 | 2 |
| C4×#16809950 | 2 |
| #27212896 | 2 |
| #27212876 | 2 |
| D4⋊(C211⋊C8) | 2 |
| #27212867 | 2 |
| #436×C211 | 2 |
| #1583 | 211 |