Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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×#20269910 | C2 | semidirect |
| 2. C2×C4⋊(C211⋊C8) | C2 | semidirect |
| 6. #27212908 | C2 | semidirect |
| 7. #389×C211 | C2 | semidirect |
| 119. C211 | #2067 | semidirect |
| 126. #389 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269910 | 2 |
| C2×C4⋊(C211⋊C8) | 2 |
| C2×#20269897 | 2 |
| #27213048 | 2 |
| #27212908 | 2 |
| #389×C211 | 2 |
| #2067 | 211 |