Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#20269901 | C2 | semidirect |
| 5. #27213053 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 7. C22×Q16×C211 | C2 | semidirect |
| 125. C211 | #2015 | semidirect |
| 127. C22×Q16 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809949 | 2 |
| C2×#20269966 | 2 |
| C2×#20269901 | 2 |
| C2×#20269899 | 2 |
| #27213053 | 2 |
| #27212900 | 2 |
| C22×Q16×C211 | 2 |
| #2015 | 211 |