Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
344 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 109 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×C4⋊(C211⋊C8) | C2 | semidirect |
| 3. C2×#20269900 | C2 | semidirect |
| 5. C4×C4⋊C4×C211 | C2 | semidirect |
| 10. #20269965 | C4 | semidirect |
| 94. C211 | #1983 | semidirect |
| 100. C4×C4⋊C4 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269965 | 2 |
| C2×C4⋊(C211⋊C8) | 2 |
| C2×#20269900 | 2 |
| C2×#20269897 | 2 |
| C4×C4⋊C4×C211 | 2 |
| #1983 | 211 |