Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
332 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 77 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. #27213203 | C2 | semidirect |
| 3. #27212889 | C2 | semidirect |
| 4. #432×C211 | C2 | semidirect |
| 12. C4⋊(C211⋊C8) | C22 | semidirect |
| 16. C4⋊C8×C211 | C22 | semidirect |
| 79. C211 | #1555 | semidirect |
| 83. #432 | D211 | semidirect |
| 94. C4⋊C8 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269974 | 2 |
| #27213203 | 2 |
| #27212889 | 2 |
| #432×C211 | 2 |
| #1555 | 211 |