Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27213356 | C2 | semidirect |
| 4. #27212899 | C2 | semidirect |
| 5. #27212891 | C2 | semidirect |
| 7. C8×Q8×C211 | C2 | semidirect |
| 78. C211 | #1682 | semidirect |
| 83. C8×Q8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213493 | 2 |
| #27213356 | 2 |
| #27213346 | 2 |
| #27212899 | 2 |
| #27212891 | 2 |
| #27212889 | 2 |
| C8×Q8×C211 | 2 |
| #1682 | 211 |