Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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. #27212992 | C2 | semidirect |
| 6. #27212905 | C2 | semidirect |
| 7. #339×C211 | C2 | semidirect |
| 10. #20269942 | C4 | semidirect |
| 11. #20269939 | C4 | semidirect |
| 17. #20269905 | C4 | semidirect |
| 18. #20269903 | C4 | semidirect |
| 37. #16809946 | C2×C4 | semidirect |
| 44. C4×Dic211 | C2×C4 | semidirect |
| 50. M16×C211 | C2×C4 | semidirect |
| 56. C42×C211 | C2×C4 | semidirect |
| 106. C211 | #1759 | semidirect |
| 114. #339 | D211 | semidirect |
| 148. M16 | C4×D211 | semidirect |
| 163. C42 | C4×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213614 | 2 |
| C2×#20269905 | 2 |
| C2×#20269903 | 2 |
| M16×Dic211 | 2 |
| #27212992 | 2 |
| #27212905 | 2 |
| #339×C211 | 2 |
| #1759 | 211 |