Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#20269888 | C2 | semidirect |
| 3. #27212885 | C2 | direct (N × H) |
| 4. C2×#97×C211 | C2 | semidirect |
| 15. #20269888 | C22 | semidirect |
| 19. #97×C211 | C22 | semidirect |
| 80. C2×C211 | #329 | semidirect |
| 85. C211 | C2×#329 | semidirect |
| 89. C2×#97 | D211 | semidirect |
| 105. #97 | C2×D211 | semidirect |
| 167. C2 | #27212885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269965 | 2 |
| C2×#20269888 | 2 |
| #27212885 | 2 |
| C2×#97×C211 | 2 |
| C2×#329 | 211 |