Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
798 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 798 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 |
|---|---|---|
| 1. C2×D8×#261 | C2 | semidirect |
| 2. #13131234 | C2 | direct (N × H) |
| 3. C2×#11718222 | C2 | semidirect |
| 4. C2×#11718276 | C2 | semidirect |
| 5. C2×#11718216 | C2 | semidirect |
| 11. D8×#261 | C22 | semidirect |
| 15. C2×C13×D16 | C4 | semidirect |
| 16. C2×#88066 | C4 | semidirect |
| 17. D13×D16 | C4 | semidirect |
| 19. C2×D208 | C4 | semidirect |
| 21. #11718276 | C22 | semidirect |
| 22. #11718222 | C22 | semidirect |
| 23. #11718216 | C22 | semidirect |
| 32. C2×C13×D8 | C2×C4 | semidirect |
| 36. D8×D13 | C2×C4 | semidirect |
| 38. C2×D104 | C2×C4 | semidirect |
| 48. C13×D16 | C2×C4 | semidirect |
| 49. C2×C13×C16 | C2×C4 | semidirect |
| 50. #88066 | C2×C4 | semidirect |
| 51. C2×#6090 | C2×C4 | semidirect |
| 52. D208 | C2×C4 | semidirect |
| 53. C16×D13 | C2×C4 | semidirect |
| 78. C13×D8 | C22×C4 | semidirect |
| 84. D104 | C22×C4 | semidirect |
| 90. C13×C16 | C22×C4 | semidirect |
| 91. #6090 | C22×C4 | semidirect |
| 133. C2×D16 | #261 | semidirect |
| 169. C2×D8 | C2×#261 | semidirect |
| 179. D16 | C2×#261 | semidirect |
| 186. C2×C16 | C2×#261 | semidirect |
| 193. C2×C13 | #2177 | semidirect |
| 196. D13 | #2177 | semidirect |
| 216. D8 | C22×#261 | semidirect |
| 233. C16 | C22×#261 | semidirect |
| 234. C13 | C2×#2177 | semidirect |
| 285. C2 | #13131234 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#261 | 2 |
| #13131234 | 2 |
| C2×#11718222 | 2 |
| C2×#11718276 | 2 |
| C2×#11718216 | 2 |
| C2×D13×D16 | 2 |
| C2×#2177 | 13 |