Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 2. C2×#20269899 | C2 | semidirect |
| 3. C2×#20269899 | C2 | semidirect |
| 4. #27213044 | C2 | semidirect |
| 5. #336×C211 | C2 | semidirect |
| 35. C4⋊Dic211 | D4 | semidirect |
| 103. C211 | #2041 | semidirect |
| 109. #336 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269974 | 2 |
| C2×#20269899 | 2 |
| #27213044 | 2 |
| #336×C211 | 2 |
| #2041 | 211 |