Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
848 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20269899 | C2 | semidirect |
| 3. #27213006 | C2 | semidirect |
| 4. C2×C22⋊C8×C211 | C2 | semidirect |
| 9. C22×D844 | C4 | semidirect |
| 11. C2×C4⋊Dic211 | C22 | semidirect |
| 16. C22×C8×C211 | C22 | semidirect |
| 56. D844 | C22⋊C4 | semidirect |
| 78. C22×C211 | #102 | semidirect |
| 101. C211 | #1786 | semidirect |
| 105. C2×C22⋊C8 | D211 | semidirect |
| 114. C22×C8 | C2×D211 | semidirect |
| 186. C22 | #20269899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D844 | 2 |
| C2×#20269899 | 2 |
| #27213006 | 2 |
| C2×C22⋊C8×C211 | 2 |
| #1786 | 211 |