Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11718580 | C2 | semidirect |
| 2. C2×#11718573 | C2 | semidirect |
| 3. #13117144 | C2 | direct (N × H) |
| 4. C2×#11718114 | C2 | semidirect |
| 5. C2×#11718041 | C2 | semidirect |
| 6. C2×#11718111 | C2 | semidirect |
| 7. C2×D13×C32 | C2 | semidirect |
| 8. C2×C13×SD64 | C2 | semidirect |
| 16. #11718580 | C22 | semidirect |
| 18. #11718573 | C22 | semidirect |
| 22. C13×SD64 | C22 | semidirect |
| 24. #11718114 | C22 | semidirect |
| 25. #11718111 | C22 | semidirect |
| 27. #11718041 | C22 | semidirect |
| 28. D13×C32 | C22 | semidirect |
| 94. C2×SD64 | D13 | semidirect |
| 136. SD64 | C2×D13 | semidirect |
| 183. C2×C13 | #2262 | semidirect |
| 217. C13 | C2×#2262 | semidirect |
| 257. C2 | #13117144 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718580 | 2 |
| C2×#11718573 | 2 |
| #13117144 | 2 |
| C2×#11718114 | 2 |
| C2×#11718041 | 2 |
| C2×#11718111 | 2 |
| C2×D13×C32 | 2 |
| C2×C13×SD64 | 2 |
| C2×#2262 | 13 |