Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
542 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D208 | C2 | semidirect |
| 2. C2×#11718111 | C2 | direct (N × H) |
| 3. C22×#88034 | C2 | semidirect |
| 4. C22×C13×D16 | C2 | semidirect |
| 8. C2×C13×D16 | C22 | semidirect |
| 11. C2×D208 | C22 | semidirect |
| 12. #11718111 | C22 | direct (N × H) |
| 13. C2×#88034 | C22 | semidirect |
| 22. C13×D16 | C23 | semidirect |
| 26. D208 | C23 | semidirect |
| 27. #88034 | C23 | semidirect |
| 45. C22×D16 | D13 | semidirect |
| 66. C2×D16 | C2×D13 | semidirect |
| 72. C22×C13 | D32 | semidirect |
| 88. D16 | C22×D13 | semidirect |
| 93. C2×C13 | C2×D32 | semidirect |
| 111. C13 | C22×D32 | semidirect |
| 129. C22 | #11718111 | direct (N × H) |
| 135. C2 | C2×#11718111 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D208 | 2 |
| C2×#11718111 | 2 |
| C22×#88034 | 2 |
| C22×C13×D16 | 2 |
| C22×D32 | 13 |