Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1022 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 267 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×#11718356 | C2 | semidirect |
| 3. #13117086 | C2 | direct (N × H) |
| 4. C2×C4×C13×C16 | C2 | semidirect |
| 11. C2×D208 | C22 | semidirect |
| 13. #11718356 | C22 | semidirect |
| 14. C4×C13×C16 | C22 | semidirect |
| 27. C2×C13×C16 | D4 | semidirect |
| 52. C13×C16 | C2×D4 | semidirect |
| 56. C2×C4×C16 | D13 | semidirect |
| 61. C2×C4×C13 | D16 | semidirect |
| 83. C4×C16 | C2×D13 | semidirect |
| 91. C4×C13 | C2×D16 | semidirect |
| 107. C2×C16 | D52 | semidirect |
| 111. C2×C13 | #2246 | semidirect |
| 134. C16 | C2×D52 | semidirect |
| 135. C13 | C2×#2246 | semidirect |
| 144. C2×C4 | D208 | semidirect |
| 160. C4 | C2×D208 | semidirect |
| 164. C2 | #13117086 | 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×#11718356 | 2 |
| #13117086 | 2 |
| C2×C4×C13×C16 | 2 |
| C2×#2246 | 13 |