Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#16809947 | C2 | semidirect |
| 2. C2×#20269973 | C2 | semidirect |
| 3. C2×#20269899 | C2 | semidirect |
| 4. C2×#20269898 | C2 | semidirect |
| 5. #27213049 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 7. C22×D8×C211 | C2 | semidirect |
| 42. C2×C211⋊C8 | D4 | semidirect |
| 61. C2×D4×C211 | D4 | semidirect |
| 66. C2×C8×C211 | D4 | semidirect |
| 81. C2×Dic211 | D8 | semidirect |
| 143. C211 | #2011 | semidirect |
| 146. C22×D8 | D211 | semidirect |
| 194. C2×D4 | C22⋊D211 | semidirect |
| 205. C2×C8 | C22⋊D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809947 | 2 |
| C2×#20269973 | 2 |
| C2×#20269899 | 2 |
| C2×#20269898 | 2 |
| #27213049 | 2 |
| #27212900 | 2 |
| C22×D8×C211 | 2 |
| #2011 | 211 |