Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27213203 | C2 | semidirect |
| 3. #27212885 | C2 | semidirect |
| 4. C4×M16×C211 | C2 | semidirect |
| 15. #20269888 | C22 | semidirect |
| 18. #97×C211 | C22 | semidirect |
| 84. C211 | #1527 | semidirect |
| 88. C4×M16 | D211 | semidirect |
| 103. #97 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269965 | 2 |
| #27213203 | 2 |
| #27212885 | 2 |
| C4×M16×C211 | 2 |
| #1527 | 211 |