Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
284 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 93 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×#20269888 | C2 | semidirect |
| 2. #27212886 | C2 | direct (N × H) |
| 6. #20269888 | C22 | semidirect |
| 60. C2×C211 | #329 | semidirect |
| 63. C211 | C2×#329 | semidirect |
| 124. C2 | #27212886 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269888 | 2 |
| #27212886 | 2 |
| C2×#124×C211 | 2 |
| C2×#329 | 211 |