Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27212892 | C2 | semidirect |
| 5. #500×C211 | C2 | semidirect |
| 46. C8×C211 | SD16 | semidirect |
| 62. C211 | #1673 | semidirect |
| 64. #500 | D211 | semidirect |
| 109. C8 | #16809949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213348 | 2 |
| C8×D844 | 2 |
| #27212899 | 2 |
| #27212892 | 2 |
| #500×C211 | 2 |
| #1673 | 211 |