Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
312 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 113 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. #27213170 | C2 | semidirect |
| 3. C4×C4⋊Dic211 | C2 | semidirect |
| 4. #27212905 | C2 | semidirect |
| 14. C4×Q8×C211 | C4 | semidirect |
| 15. C4×Q8×C211 | C4 | semidirect |
| 18. C4×D4×C211 | C4 | semidirect |
| 19. C4×D4×C211 | C4 | semidirect |
| 65. Q8×C211 | C4⋊C4 | semidirect |
| 69. D4×C211 | C4⋊C4 | semidirect |
| 103. C4×C211 | #104 | semidirect |
| 115. C211 | #1806 | semidirect |
| 124. C4×Q8 | Dic211 | semidirect |
| 125. C4×Q8 | Dic211 | semidirect |
| 128. C4×D4 | Dic211 | semidirect |
| 129. C4×D4 | Dic211 | semidirect |
| 177. Q8 | C4⋊Dic211 | semidirect |
| 181. D4 | C4⋊Dic211 | semidirect |
| 220. C4 | #20269904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213170 | 2 |
| C2×#20269904 | 2 |
| C4×C4⋊Dic211 | 2 |
| #27212905 | 2 |
| C4×#41×C211 | 2 |
| #1806 | 211 |