Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
384 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#20269897 | C2 | semidirect |
| 3. C2×C8×Dic211 | C2 | semidirect |
| 4. #27213047 | C2 | semidirect |
| 5. C2×#107×C211 | C2 | semidirect |
| 9. C2×D1688 | C4 | semidirect |
| 51. C2×Dic211 | D8 | semidirect |
| 62. C8×C211 | C22⋊C4 | semidirect |
| 85. C211 | #1970 | semidirect |
| 88. C2×#107 | D211 | semidirect |
| 148. C8 | (C2×D211)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1688 | 2 |
| C2×#20269897 | 2 |
| C2×C8×Dic211 | 2 |
| #27213047 | 2 |
| C2×#107×C211 | 2 |
| #1970 | 211 |