Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27213195 | C2 | semidirect |
| 3. #27213150 | C2 | semidirect |
| 4. #27213130 | C2 | semidirect |
| 5. C2×#20269893 | C2 | semidirect |
| 6. #27212916 | C2 | semidirect |
| 7. #421×C211 | C2 | semidirect |
| 110. C211 | #2048 | semidirect |
| 114. #421 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20270002 | 2 |
| #27213195 | 2 |
| #27213150 | 2 |
| #27213130 | 2 |
| C2×#20269893 | 2 |
| #27212916 | 2 |
| #421×C211 | 2 |
| #2048 | 211 |