Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
| 5. #27212908 | C2 | semidirect |
| 6. #27212901 | C2 | semidirect |
| 7. #389×C211 | C2 | semidirect |
| 18. #20269897 | C4 | semidirect |
| 40. C2×C211⋊C8 | C2×C4 | semidirect |
| 53. C4⋊C4×C211 | C2×C4 | semidirect |
| 66. D844 | C4⋊C4 | semidirect |
| 123. C211 | #1864 | semidirect |
| 129. #389 | D211 | semidirect |
| 176. C4⋊C4 | C4×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D844 | 2 |
| C2×#20269908 | 2 |
| C2×#20269897 | 2 |
| #27212908 | 2 |
| #27212901 | 2 |
| #389×C211 | 2 |
| #1864 | 211 |