Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 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×#20269908 | C2 | semidirect |
| 4. #27212909 | C2 | semidirect |
| 5. #340×C211 | C2 | semidirect |
| 9. C2×C8×D211 | C4 | semidirect |
| 48. C211⋊C8 | C22⋊C4 | semidirect |
| 67. C2×D211 | #106 | semidirect |
| 80. C211 | #1807 | semidirect |
| 86. #340 | D211 | 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×#20269908 | 2 |
| #27213003 | 2 |
| #27212909 | 2 |
| #340×C211 | 2 |
| #1807 | 211 |