Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
302 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 78 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. D13⋊M64 | C2 | semidirect |
| 2. C2×#11718222 | C2 | semidirect |
| 3. #13129990 | C2 | semidirect |
| 4. #13129989 | C2 | semidirect |
| 8. C13×#508 | C4 | semidirect |
| 11. D13×Q32 | C4 | semidirect |
| 15. D13×D16 | C4 | semidirect |
| 16. #11718565 | C4 | semidirect |
| 20. #11718222 | C22 | semidirect |
| 21. #11718214 | C22 | semidirect |
| 37. C13×Q32 | C2×C4 | semidirect |
| 39. C13×D16 | C2×C4 | semidirect |
| 46. Dic104 | C2×C4 | semidirect |
| 48. D208 | C2×C4 | semidirect |
| 129. #508 | #261 | semidirect |
| 168. Q32 | C2×#261 | semidirect |
| 175. D16 | C2×#261 | semidirect |
| 190. D13 | #1418 | semidirect |
| 225. C13 | C2×#1418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13⋊M64 | 2 |
| C2×#11718222 | 2 |
| #13129990 | 2 |
| #13129989 | 2 |
| D13×#508 | 2 |
| C2×#1418 | 13 |