Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
670 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 2. #13131233 | C2 | direct (N × H) |
| 15. C2×C13×Q32 | C4 | semidirect |
| 16. C2×#88069 | C4 | semidirect |
| 17. D13×Q32 | C4 | semidirect |
| 19. C2×Dic104 | C4 | semidirect |
| 48. C13×Q32 | C2×C4 | semidirect |
| 50. #88069 | C2×C4 | semidirect |
| 52. Dic104 | C2×C4 | semidirect |
| 129. C2×Q32 | #261 | semidirect |
| 170. Q32 | C2×#261 | semidirect |
| 183. C2×C13 | #2176 | semidirect |
| 185. D13 | #2176 | semidirect |
| 222. C13 | C2×#2176 | semidirect |
| 263. C2 | #13131233 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#261 | 2 |
| #13131233 | 2 |
| C2×#11718222 | 2 |
| C2×#11718280 | 2 |
| C2×#11718216 | 2 |
| C2×D13×Q32 | 2 |
| C2×#2176 | 13 |