Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#20269903 | C2 | semidirect |
| 3. C42×Dic211 | C2 | semidirect |
| 4. #423×C211 | C2 | semidirect |
| 6. #20269977 | C4 | semidirect |
| 7. #20269974 | C4 | semidirect |
| 8. #20269965 | C4 | semidirect |
| 29. C4×Dic211 | D4 | semidirect |
| 62. C4×C211 | #104 | semidirect |
| 72. C211 | #1962 | semidirect |
| 75. #423 | D211 | semidirect |
| 137. C4 | #20269903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213696 | 2 |
| C2×#20269903 | 2 |
| C42×Dic211 | 2 |
| #423×C211 | 2 |
| #1962 | 211 |