Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
372 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4⋊(C211⋊C8) | C2 | semidirect |
| 3. #27213016 | C2 | semidirect |
| 4. #27212908 | C2 | semidirect |
| 15. C4×D4×C211 | C4 | semidirect |
| 61. D4×C211 | C4⋊C4 | semidirect |
| 94. C4×C211 | #102 | semidirect |
| 108. C211 | #1802 | semidirect |
| 119. C4×D4 | Dic211 | semidirect |
| 166. D4 | C4⋊Dic211 | semidirect |
| 204. C4 | #20269898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C211⋊C8) | 2 |
| C2×#20269898 | 2 |
| #27213016 | 2 |
| #27212908 | 2 |
| C2×C4×D4×C211 | 2 |
| #1802 | 211 |