Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 4. #27213053 | C2 | semidirect |
| 5. #27212908 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 7. C2×#103×C211 | C2 | semidirect |
| 12. C2×#16809949 | C4 | semidirect |
| 42. C2×C211⋊C8 | C2×C4 | semidirect |
| 53. C2×Q8×C211 | C2×C4 | semidirect |
| 81. C2×Dic211 | SD16 | semidirect |
| 133. C211 | #1877 | semidirect |
| 137. C2×#103 | D211 | semidirect |
| 166. C2×Q8 | C4×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809949 | 2 |
| C2×#20269939 | 2 |
| C2×#20269899 | 2 |
| #27213053 | 2 |
| #27212908 | 2 |
| #27212900 | 2 |
| C2×#103×C211 | 2 |
| #1877 | 211 |