Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
702 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 280 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 |
|---|---|---|
| 3. C2×#11718219 | C2 | direct (N × H) |
| 12. C22×C13×C16 | C4 | semidirect |
| 13. C22×#6090 | C4 | semidirect |
| 14. C2×#88038 | C4 | semidirect |
| 16. #11718219 | C22 | direct (N × H) |
| 34. C2×C13×C16 | C2×C4 | semidirect |
| 35. C2×#6090 | C2×C4 | semidirect |
| 36. #88038 | C2×C4 | semidirect |
| 62. C13×C16 | C22×C4 | semidirect |
| 63. #6090 | C22×C4 | semidirect |
| 94. C22×C16 | #261 | semidirect |
| 100. C22×C13 | #365 | semidirect |
| 127. C2×C16 | C2×#261 | semidirect |
| 132. C2×C13 | C2×#365 | semidirect |
| 160. C16 | C22×#261 | semidirect |
| 161. C13 | C22×#365 | semidirect |
| 186. C22 | #11718219 | direct (N × H) |
| 195. C2 | C2×#11718219 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88103 | 2 |
| C22×#88101 | 2 |
| C2×#11718219 | 2 |
| C22×#88038 | 2 |
| C22×#365 | 13 |