Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C2×#20269909 | C2 | semidirect |
| 5. C4×C4⋊Dic211 | C2 | semidirect |
| 6. #27212909 | C2 | semidirect |
| 7. #336×C211 | C2 | semidirect |
| 17. #20269899 | C4 | semidirect |
| 118. C211 | #1926 | semidirect |
| 126. #336 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269909 | 2 |
| C2×#20269899 | 2 |
| #27213048 | 2 |
| C4×C4⋊Dic211 | 2 |
| #27212909 | 2 |
| #336×C211 | 2 |
| #1926 | 211 |