Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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×#88038 | C2 | semidirect |
| 2. C2×#11718818 | C2 | semidirect |
| 3. #13116936 | C2 | direct (N × H) |
| 4. C2×#11718097 | C2 | semidirect |
| 5. C2×#11718154 | C2 | semidirect |
| 6. C22×C13×D16 | C2 | semidirect |
| 11. C2×C13×D16 | C22 | semidirect |
| 15. #11718818 | C22 | semidirect |
| 19. C2×#88038 | C22 | semidirect |
| 20. #11718154 | C22 | semidirect |
| 21. #11718097 | C22 | semidirect |
| 40. C2×C13×C16 | D4 | semidirect |
| 79. C13×C16 | C2×D4 | semidirect |
| 81. C22×D16 | D13 | semidirect |
| 118. C2×D16 | C2×D13 | semidirect |
| 165. C2×C16 | C22⋊D13 | semidirect |
| 171. C2×C13 | #2218 | semidirect |
| 206. C16 | C2×C22⋊D13 | semidirect |
| 207. C13 | C2×#2218 | semidirect |
| 252. C2 | #13116936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88038 | 2 |
| C2×#11718818 | 2 |
| #13116936 | 2 |
| C2×#11718097 | 2 |
| C2×#11718154 | 2 |
| C22×C13×D16 | 2 |
| C2×#2218 | 13 |