Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C2×#20269910 | C2 | semidirect |
| 4. C2×#20269887 | C2 | semidirect |
| 5. #27213053 | C2 | semidirect |
| 7. C2×#103×C211 | C2 | semidirect |
| 11. C2×#16809949 | C4 | semidirect |
| 70. C211⋊C8 | C22⋊C4 | semidirect |
| 112. C211 | #1973 | semidirect |
| 116. C2×#103 | 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×#20269910 | 2 |
| C2×#20269899 | 2 |
| C2×#20269887 | 2 |
| #27213053 | 2 |
| #27213047 | 2 |
| C2×#103×C211 | 2 |
| #1973 | 211 |