Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#20269910 | C2 | semidirect |
| 5. #27212914 | C2 | semidirect |
| 6. #27212910 | C2 | semidirect |
| 7. #343×C211 | C2 | semidirect |
| 94. C211 | #2078 | semidirect |
| 101. #343 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269910 | 2 |
| #27213148 | 2 |
| #27213145 | 2 |
| #27213114 | 2 |
| #27212914 | 2 |
| #27212910 | 2 |
| #343×C211 | 2 |
| #2078 | 211 |