Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1146 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 251 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×#11718356 | C2 | semidirect |
| 2. C2×#11718734 | C2 | semidirect |
| 3. C2×#11718749 | C2 | semidirect |
| 4. #13114500 | C2 | direct (N × H) |
| 5. C2×#11718047 | C2 | semidirect |
| 6. C2×C13×#492 | C2 | semidirect |
| 14. C13×#492 | C22 | semidirect |
| 17. #11718749 | C22 | semidirect |
| 19. #11718734 | C22 | semidirect |
| 23. #11718356 | C22 | semidirect |
| 24. #11718047 | C22 | semidirect |
| 81. C2×C8×C13 | D8 | semidirect |
| 94. C2×#492 | D13 | semidirect |
| 126. C8×C13 | C2×D8 | semidirect |
| 139. #492 | C2×D13 | semidirect |
| 193. C2×C13 | #1721 | semidirect |
| 225. C2×C8 | #6104 | semidirect |
| 232. C13 | C2×#1721 | semidirect |
| 262. C8 | C2×#6104 | semidirect |
| 280. C2 | #13114500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718356 | 2 |
| C2×#11718734 | 2 |
| C2×#11718749 | 2 |
| #13114500 | 2 |
| C2×#11718047 | 2 |
| C2×C13×#492 | 2 |
| C2×#1721 | 13 |