Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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×#11718562 | C2 | semidirect |
| 2. #13124480 | C2 | semidirect |
| 3. #13116936 | C2 | semidirect |
| 4. #13116919 | C2 | semidirect |
| 5. #13116620 | C2 | semidirect |
| 6. #13116552 | C2 | semidirect |
| 7. C22×C13×D16 | C2 | semidirect |
| 17. #11718818 | C22 | semidirect |
| 21. C2×#88038 | C22 | semidirect |
| 22. C2×C16×D13 | C22 | semidirect |
| 23. #11718154 | C22 | semidirect |
| 24. #11718097 | C22 | semidirect |
| 25. #11718096 | C22 | semidirect |
| 45. C2×C13×C16 | D4 | semidirect |
| 88. C22×D16 | D13 | semidirect |
| 173. C2×C16 | C22⋊D13 | semidirect |
| 216. C13 | #33607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718562 | 2 |
| #13124480 | 2 |
| #13116936 | 2 |
| #13116919 | 2 |
| #13116620 | 2 |
| #13116552 | 2 |
| C22×C13×D16 | 2 |
| #33607 | 13 |