Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #27212893 | C2 | semidirect |
| 5. #27212892 | C2 | semidirect |
| 6. #27212891 | C2 | semidirect |
| 7. #332×C211 | C2 | semidirect |
| 91. C211 | #1546 | semidirect |
| 99. #332 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D211 | 2 |
| #27213198 | 2 |
| #27213168 | 2 |
| #27212893 | 2 |
| #27212892 | 2 |
| #27212891 | 2 |
| #332×C211 | 2 |
| #1546 | 211 |