Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
272 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 14. #20269910 | C4 | semidirect |
| 15. #20269908 | C4 | semidirect |
| 16. #20269887 | C4 | semidirect |
| 59. C211⋊C8 | C42 | semidirect |
| 98. C211 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269910 | 2 |
| C2×#20269908 | 2 |
| C2×#20269887 | 2 |
| C4⋊C4×Dic211 | 2 |
| #27212909 | 2 |
| #340×C211 | 2 |
| #1776 | 211 |