Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#11718575 | C2 | semidirect |
| 2. #13125265 | C2 | semidirect |
| 3. D13×#493 | C2 | semidirect |
| 4. #13117101 | C2 | semidirect |
| 5. #13117093 | C2 | semidirect |
| 6. #13117086 | C2 | semidirect |
| 7. #13117085 | C2 | semidirect |
| 8. C4×#88038 | C2 | semidirect |
| 9. C13×#2248 | C2 | semidirect |
| 16. C2×C13×SD32 | C22 | semidirect |
| 17. C13×#494 | C22 | semidirect |
| 20. #11718852 | C22 | semidirect |
| 21. C2×#88068 | C22 | semidirect |
| 24. C2×#88066 | C22 | semidirect |
| 28. C2×D208 | C22 | semidirect |
| 31. #11718356 | C22 | semidirect |
| 33. C4×C13×C16 | C22 | semidirect |
| 34. #11718094 | C22 | semidirect |
| 35. C4×#6090 | C22 | semidirect |
| 77. #88038 | D4 | semidirect |
| 121. C13×C16 | C2×D4 | semidirect |
| 122. #6090 | C2×D4 | semidirect |
| 128. #2248 | D13 | semidirect |
| 173. C2×SD32 | C2×D13 | semidirect |
| 179. #494 | C2×D13 | semidirect |
| 190. C4×C16 | C2×D13 | semidirect |
| 202. C4×C13 | #509 | semidirect |
| 298. C16 | D4×D13 | semidirect |
| 299. C13 | #33717 | semidirect |
| 346. C4 | #11718575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718575 | 2 |
| #13125265 | 2 |
| D13×#493 | 2 |
| #13117101 | 2 |
| #13117093 | 2 |
| #13117086 | 2 |
| #13117085 | 2 |
| C4×#88038 | 2 |
| C13×#2248 | 2 |
| #33717 | 13 |