Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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×#20269909 | C2 | semidirect |
| 4. #27212908 | C2 | semidirect |
| 5. C2×#106×C211 | C2 | semidirect |
| 10. C2×C8×D211 | C4 | semidirect |
| 67. C8×C211 | C22⋊C4 | semidirect |
| 77. C2×D211 | #106 | semidirect |
| 91. C211 | #1807 | semidirect |
| 95. C2×#106 | D211 | semidirect |
| 159. 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×C8×D211 | 2 |
| C2×#20269909 | 2 |
| #27213003 | 2 |
| #27212908 | 2 |
| C2×#106×C211 | 2 |
| #1807 | 211 |