Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
336 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×C8×C211 | C2 | semidirect |
| 13. (C2×D211)⋊C8 | C4 | semidirect |
| 77. C211 | #1750 | semidirect |
| 82. C2×C4×C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269934 | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| C2×#20269888 | 2 |
| #27212900 | 2 |
| C2×C4×C8×C211 | 2 |
| #1750 | 211 |