Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27213170 | C2 | semidirect |
| 3. C2×#20269905 | C2 | semidirect |
| 4. C43×C211 | C2 | semidirect |
| 7. #20269977 | C4 | semidirect |
| 8. #20269974 | C4 | semidirect |
| 9. #20269965 | C4 | semidirect |
| 36. C42×C211 | D4 | semidirect |
| 63. C4×C211 | #104 | semidirect |
| 72. C211 | #1962 | semidirect |
| 77. C43 | D211 | semidirect |
| 109. C42 | D844 | semidirect |
| 137. C4 | #20269905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213696 | 2 |
| #27213170 | 2 |
| C2×#20269905 | 2 |
| C43×C211 | 2 |
| #1962 | 211 |