Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
326 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 91 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×#20269977 | C2 | semidirect |
| 4. #27212909 | C2 | semidirect |
| 5. #336×C211 | C2 | semidirect |
| 24. C2×D844 | Q8 | semidirect |
| 96. C211 | #2023 | semidirect |
| 102. #336 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269977 | 2 |
| C2×#20269899 | 2 |
| #27213048 | 2 |
| #27212909 | 2 |
| #336×C211 | 2 |
| #2023 | 211 |