Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 2. #27213170 | C2 | semidirect |
| 3. C2×#20269895 | C2 | semidirect |
| 5. C4×M16×C211 | C2 | semidirect |
| 80. C211 | #1967 | semidirect |
| 86. C4×M16 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269965 | 2 |
| #27213170 | 2 |
| C2×#20269895 | 2 |
| C2×#20269893 | 2 |
| C4×M16×C211 | 2 |
| #1967 | 211 |