Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 8. C4×Dic422 | C4 | semidirect |
| 14. #20269902 | C4 | direct (N × H) |
| 43. Dic422 | C42 | semidirect |
| 68. C4×C211 | #103 | semidirect |
| 80. C211 | C4×#103 | semidirect |
| 152. C4 | #20269902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic422 | 2 |
| C2×#20269902 | 2 |
| C4×C4⋊Dic211 | 2 |
| #27212909 | 2 |
| C2×C4×C8×C211 | 2 |
| C4×#103 | 211 |