Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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×#20269912 | C2 | semidirect |
| 5. #27212911 | C2 | semidirect |
| 6. #27212910 | C2 | semidirect |
| 7. C2×#108×C211 | C2 | semidirect |
| 99. C2×D211 | #108 | semidirect |
| 113. C211 | #1855 | semidirect |
| 117. C2×#108 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D211 | 2 |
| C2×#20269912 | 2 |
| #27213109 | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| #27212911 | 2 |
| #27212910 | 2 |
| C2×#108×C211 | 2 |
| #1855 | 211 |