Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27213011 | C2 | semidirect |
| 5. #27212914 | C2 | semidirect |
| 6. #27212905 | C2 | semidirect |
| 7. #428×C211 | C2 | semidirect |
| 17. #20269903 | C4 | semidirect |
| 46. C4×Dic211 | C2×C4 | semidirect |
| 50. M16×C211 | C2×C4 | semidirect |
| 111. C211 | #1860 | semidirect |
| 114. #428 | D211 | semidirect |
| 154. M16 | C4×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213626 | 2 |
| C2×#20269903 | 2 |
| #27213145 | 2 |
| #27213011 | 2 |
| #27212914 | 2 |
| #27212905 | 2 |
| #428×C211 | 2 |
| #1860 | 211 |