Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
344 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #27213199 | C2 | semidirect |
| 2. #27213170 | C2 | semidirect |
| 3. #27212890 | C2 | semidirect |
| 7. C4⋊(C211⋊C8) | C22 | semidirect |
| 8. C4⋊(C211⋊C8) | C22 | semidirect |
| 84. C211 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213199 | 2 |
| #27213170 | 2 |
| #27212890 | 2 |
| C2×#127×C211 | 2 |
| #1545 | 211 |