Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×Dic422 | C2 | semidirect |
| 4. #27212897 | C2 | semidirect |
| 5. #27212878 | C2 | semidirect |
| 7. C82×C211 | C2 | semidirect |
| 26. #16809951 | C8 | direct (N × H) |
| 43. Dic422 | C2×C8 | semidirect |
| 59. C8×C211 | C2×C8 | semidirect |
| 60. C8×C211 | SD16 | semidirect |
| 77. C211 | C8×SD16 | semidirect |
| 85. C82 | D211 | semidirect |
| 137. C8 | C8×D211 | semidirect |
| 138. C8 | #16809951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic422 | 2 |
| C4×#16809951 | 2 |
| C8×D844 | 2 |
| #27212897 | 2 |
| #27212878 | 2 |
| #27212875 | 2 |
| C82×C211 | 2 |
| C8×SD16 | 211 |