Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20269888 | C2 | semidirect |
| 4. #27212900 | C2 | semidirect |
| 5. C2×#97×C211 | C2 | semidirect |
| 13. (C2×D211)⋊C8 | C4 | semidirect |
| 30. C2×C211⋊C8 | C2×C4 | semidirect |
| 38. C2×C8×C211 | C2×C4 | semidirect |
| 74. C2×D211 | #97 | semidirect |
| 86. C211 | #1749 | semidirect |
| 91. C2×#97 | D211 | semidirect |
| 122. C2×C8 | C4×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D211 | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| C2×#20269888 | 2 |
| #27212900 | 2 |
| C2×#97×C211 | 2 |
| #1749 | 211 |