Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27213223 | C2 | semidirect |
| 3. #27212873 | C2 | semidirect |
| 4. #27212867 | C2 | semidirect |
| 5. #334×C211 | C2 | semidirect |
| 41. C8×C211 | M16 | semidirect |
| 55. C211 | #1594 | semidirect |
| 59. #334 | D211 | semidirect |
| 97. C8 | #16809945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1688 | 2 |
| #27213223 | 2 |
| #27212873 | 2 |
| #27212867 | 2 |
| #334×C211 | 2 |
| #1594 | 211 |