Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 85. C2×C4×C211 | Q16 | semidirect |
| 116. C211 | #2056 | semidirect |
| 200. C2×C4 | #16809952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809952 | 2 |
| C2×C4⋊(C211⋊C8) | 2 |
| C2×#20269901 | 2 |
| C2×#20269900 | 2 |
| #27213052 | 2 |
| #27212908 | 2 |
| #391×C211 | 2 |
| #2056 | 211 |