Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
514 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. C4×#88100 | C2 | semidirect |
| 4. #13130048 | C2 | semidirect |
| 5. #13129668 | C2 | semidirect |
| 6. #13129663 | C2 | semidirect |
| 9. Q8×#1057 | C4 | semidirect |
| 13. #11719073 | C4 | semidirect |
| 25. C13×Q8⋊C8 | C4 | semidirect |
| 26. Q8⋊#1055 | C4 | semidirect |
| 27. #11718075 | C4 | semidirect |
| 28. #11718051 | C4 | semidirect |
| 125. Q8×C13 | #97 | semidirect |
| 137. D52 | #97 | semidirect |
| 150. #1057 | #104 | semidirect |
| 171. Q8⋊C8 | #261 | semidirect |
| 282. C13 | #8192 | semidirect |
| 286. Q8 | #88100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131642 | 2 |
| C4×#88118 | 2 |
| C4×#88100 | 2 |
| #13130048 | 2 |
| #13129668 | 2 |
| #13129663 | 2 |
| #13113217 | 2 |
| #8192 | 13 |