Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1716 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×#11719422 | C2 | semidirect |
| 2. #13124923 | C2 | semidirect |
| 3. #13113950 | C2 | semidirect |
| 4. #13113888 | C2 | semidirect |
| 5. #13113550 | C2 | semidirect |
| 6. #13113280 | C2 | semidirect |
| 7. C13×#3151 | C2 | semidirect |
| 10. C13×#532 | C22 | semidirect |
| 19. C13×#493 | C22 | semidirect |
| 20. C13×#492 | C22 | semidirect |
| 21. C4×C13×M16 | C22 | semidirect |
| 22. #11718745 | C22 | semidirect |
| 23. #11718733 | C22 | semidirect |
| 27. #11718587 | C22 | semidirect |
| 28. #11718136 | C22 | semidirect |
| 29. #11718051 | C22 | semidirect |
| 44. C13×C4⋊Q8 | C23 | semidirect |
| 48. C13×#127 | C23 | semidirect |
| 66. C4×C8×C13 | C23 | semidirect |
| 71. C4⋊#1055 | C23 | semidirect |
| 122. #3151 | D13 | semidirect |
| 161. D52 | AGL(1,ℤ/8) | semidirect |
| 171. #532 | C2×D13 | semidirect |
| 177. #493 | C2×D13 | semidirect |
| 178. #492 | C2×D13 | semidirect |
| 185. C4×M16 | C2×D13 | semidirect |
| 222. C4⋊Q8 | C22×D13 | semidirect |
| 226. #127 | C22×D13 | semidirect |
| 249. C4×C8 | C22×D13 | semidirect |
| 303. C13 | #18524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719422 | 2 |
| #13124923 | 2 |
| #13113950 | 2 |
| #13113888 | 2 |
| #13113550 | 2 |
| #13113280 | 2 |
| C13×#3151 | 2 |
| #18524 | 13 |