Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27213276 | C2 | semidirect |
| 4. #27212899 | C2 | semidirect |
| 5. #27212878 | C2 | semidirect |
| 7. #322×C211 | C2 | semidirect |
| 60. C8×C211 | M16 | semidirect |
| 77. C211 | #1592 | semidirect |
| 85. #322 | D211 | semidirect |
| 138. C8 | #16809945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213276 | 2 |
| C4×#16809951 | 2 |
| #27213225 | 2 |
| #27212899 | 2 |
| #27212878 | 2 |
| #27212875 | 2 |
| #322×C211 | 2 |
| #1592 | 211 |