Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 4. M16×Dic211 | C2 | semidirect |
| 5. #27212917 | C2 | semidirect |
| 6. #27212907 | C2 | semidirect |
| 7. #430×C211 | C2 | semidirect |
| 15. #20269895 | C4 | semidirect |
| 16. #20269893 | C4 | semidirect |
| 95. C211 | #1932 | semidirect |
| 97. #430 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213162 | 2 |
| C2×#20269903 | 2 |
| #27213128 | 2 |
| M16×Dic211 | 2 |
| #27212917 | 2 |
| #27212907 | 2 |
| #430×C211 | 2 |
| #1932 | 211 |