Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
820 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 820 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 |
|---|---|---|
| 1. C2×#20269894 | C2 | semidirect |
| 2. #27213110 | C2 | semidirect |
| 4. C2×#16809946 | C22 | semidirect |
| 59. C22×C211 | #100 | semidirect |
| 69. C211 | #1783 | semidirect |
| 129. C22 | #20269894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269894 | 2 |
| #27213110 | 2 |
| C23×D4×C211 | 2 |
| #1783 | 211 |