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. C22×D208 | C2 | semidirect |
| 2. C2×#11718562 | C2 | semidirect |
| 3. #13124485 | C2 | semidirect |
| 4. #13116940 | C2 | semidirect |
| 5. #13116923 | C2 | semidirect |
| 6. #13116551 | C2 | semidirect |
| 7. C13×#2158 | C2 | semidirect |
| 19. C2×#88038 | C22 | semidirect |
| 20. C2×C16×D13 | C22 | semidirect |
| 21. #11718544 | C22 | semidirect |
| 23. C13×#367 | C22 | semidirect |
| 24. C13×#366 | C22 | semidirect |
| 25. #11718083 | C22 | semidirect |
| 43. C2×C13×C16 | D4 | semidirect |
| 93. #2158 | D13 | semidirect |
| 134. #367 | C2×D13 | semidirect |
| 135. #366 | C2×D13 | semidirect |
| 173. C2×C16 | D52 | semidirect |
| 216. C13 | #33607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D208 | 2 |
| C2×#11718562 | 2 |
| #13124485 | 2 |
| #13116940 | 2 |
| #13116923 | 2 |
| #13116551 | 2 |
| C13×#2158 | 2 |
| #33607 | 13 |