Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#20269887 | C2 | semidirect |
| 5. #27212901 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 7. C2×#97×C211 | C2 | semidirect |
| 13. C2×C8×D211 | C4 | semidirect |
| 16. (C2×D211)⋊C8 | C4 | semidirect |
| 80. C8×C211 | C22⋊C4 | semidirect |
| 90. C2×D211 | #97 | semidirect |
| 104. C211 | #1752 | semidirect |
| 109. C2×#97 | D211 | semidirect |
| 185. C8 | (C2×D211)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D211 | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| C2×#20269887 | 2 |
| C4×(C2×D211)⋊C4 | 2 |
| #27212901 | 2 |
| #27212900 | 2 |
| C2×#97×C211 | 2 |
| #1752 | 211 |