Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #13125574 | C2 | semidirect |
| 2. #13117050 | C2 | semidirect |
| 3. #13117007 | C2 | semidirect |
| 4. #13116912 | C2 | semidirect |
| 5. #13116782 | C2 | semidirect |
| 6. #13116734 | C2 | semidirect |
| 7. #13116648 | C2 | semidirect |
| 8. C13×#2956 | C2 | semidirect |
| 23. #11718372 | C22 | semidirect |
| 24. #11718356 | C22 | semidirect |
| 26. #11718341 | C22 | semidirect |
| 29. #11718087 | C22 | semidirect |
| 30. #11718086 | C22 | semidirect |
| 31. #11718058 | C22 | semidirect |
| 32. #11718055 | C22 | semidirect |
| 90. C13×Q16 | #41 | semidirect |
| 94. C13×D8 | #41 | semidirect |
| 119. #2956 | D13 | semidirect |
| 258. Q16 | #6127 | semidirect |
| 264. D8 | #6127 | semidirect |
| 286. C13 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125574 | 2 |
| #13117050 | 2 |
| #13117007 | 2 |
| #13116912 | 2 |
| #13116782 | 2 |
| #13116734 | 2 |
| #13116648 | 2 |
| C13×#2956 | 2 |
| #33688 | 13 |