Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 9. #20269913 | C4 | semidirect |
| 15. #108×C211 | C4 | semidirect |
| 56. Dic211 | #108 | direct (N × H) |
| 61. C211 | C4×#108 | semidirect |
| 74. #108 | Dic211 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269913 | 2 |
| M16×Dic211 | 2 |
| C2×C8×Dic211 | 2 |
| #27212910 | 2 |
| C2×#108×C211 | 2 |
| C4×#108 | 211 |