Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #27212899 | C2 | semidirect |
| 4. #27212898 | C2 | semidirect |
| 5. #335×C211 | C2 | semidirect |
| 44. C211⋊C8 | M16 | semidirect |
| 50. C8×C211 | M16 | semidirect |
| 67. C211 | #1567 | semidirect |
| 73. #335 | D211 | semidirect |
| 118. C8 | #16809945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213168 | 2 |
| C4×C8×D211 | 2 |
| #27212899 | 2 |
| #27212898 | 2 |
| #335×C211 | 2 |
| #1567 | 211 |