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×D208 | C2 | semidirect |
| 2. C22×#88038 | C2 | semidirect |
| 3. C2×#11718544 | C2 | semidirect |
| 4. #13116940 | C2 | direct (N × H) |
| 5. C2×#11718083 | C2 | semidirect |
| 6. C2×C13×#367 | C2 | semidirect |
| 15. C2×D208 | C22 | semidirect |
| 17. C2×#88038 | C22 | semidirect |
| 19. #11718544 | C22 | semidirect |
| 20. C13×#367 | C22 | semidirect |
| 21. #11718083 | C22 | semidirect |
| 39. C2×C13×C16 | D4 | semidirect |
| 79. C13×C16 | C2×D4 | semidirect |
| 85. C2×#367 | D13 | semidirect |
| 127. #367 | C2×D13 | semidirect |
| 165. C2×C16 | D52 | semidirect |
| 170. C2×C13 | #2218 | semidirect |
| 206. C16 | C2×D52 | semidirect |
| 207. C13 | C2×#2218 | semidirect |
| 252. C2 | #13116940 | 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 |
| C22×#88038 | 2 |
| C2×#11718544 | 2 |
| #13116940 | 2 |
| C2×#11718083 | 2 |
| C2×C13×#367 | 2 |
| C2×#2218 | 13 |