Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27213881 | C2 | semidirect |
| 3. #27213347 | C2 | semidirect |
| 4. #27213346 | C2 | semidirect |
| 5. #27212889 | C2 | semidirect |
| 6. #27212878 | C2 | semidirect |
| 7. Q8⋊C8×C211 | C2 | semidirect |
| 98. C211 | #1620 | semidirect |
| 106. Q8⋊C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213881 | 2 |
| #27213523 | 2 |
| #27213347 | 2 |
| #27213346 | 2 |
| #27212889 | 2 |
| #27212878 | 2 |
| Q8⋊C8×C211 | 2 |
| #1620 | 211 |