Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 151 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. #13127977 | C2 | semidirect |
| 2. #13117154 | C2 | semidirect |
| 3. #13117148 | C2 | semidirect |
| 4. #13117143 | C2 | semidirect |
| 5. C2×#11718113 | C2 | semidirect |
| 6. #13117130 | C2 | semidirect |
| 7. C13×#3417 | C2 | semidirect |
| 11. C13×#508 | C22 | semidirect |
| 12. C2×C13×Q32 | C22 | semidirect |
| 17. #11718114 | C22 | semidirect |
| 18. #11718113 | C22 | semidirect |
| 19. #11718113 | C22 | semidirect |
| 20. #11718112 | C22 | semidirect |
| 21. #11718111 | C22 | semidirect |
| 22. #11718091 | C22 | semidirect |
| 23. C2×#88034 | C22 | semidirect |
| 67. #3417 | D13 | semidirect |
| 96. #508 | C2×D13 | semidirect |
| 97. C2×Q32 | C2×D13 | semidirect |
| 161. C13 | #33983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127977 | 2 |
| #13117154 | 2 |
| #13117148 | 2 |
| #13117143 | 2 |
| C2×#11718113 | 2 |
| #13117130 | 2 |
| C13×#3417 | 2 |
| #33983 | 13 |