Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C2×#20269912 | C2 | semidirect |
| 2. #27213186 | C2 | semidirect |
| 3. #27213174 | C2 | semidirect |
| 7. #343×C211 | C2 | semidirect |
| 97. C211 | #2063 | semidirect |
| 105. #343 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269912 | 2 |
| #27213186 | 2 |
| #27213174 | 2 |
| #27213152 | 2 |
| C2×#20269897 | 2 |
| C2×#20269893 | 2 |
| #343×C211 | 2 |
| #2063 | 211 |