Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
396 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 87 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. #27213169 | C2 | semidirect |
| 3. C2×#20269894 | C2 | semidirect |
| 4. C2×#20269893 | C2 | semidirect |
| 5. C2×#20269893 | C2 | semidirect |
| 6. M16×Dic211 | C2 | semidirect |
| 7. C2×#100×C211 | C2 | semidirect |
| 40. #16809946 | D4 | semidirect |
| 57. M16×C211 | D4 | semidirect |
| 109. Dic211 | #100 | semidirect |
| 116. C211 | #1965 | semidirect |
| 123. C2×#100 | D211 | semidirect |
| 169. M16 | C22⋊D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269973 | 2 |
| #27213169 | 2 |
| C2×#20269894 | 2 |
| C2×#20269893 | 2 |
| M16×Dic211 | 2 |
| C2×#100×C211 | 2 |
| #1965 | 211 |