Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
782 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 320 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. C2×#11718222 | C2 | direct (N × H) |
| 8. C22×C13×C16 | C4 | semidirect |
| 9. C22×#6090 | C4 | semidirect |
| 10. C2×C16×D13 | C4 | semidirect |
| 12. #11718222 | C22 | direct (N × H) |
| 25. C2×C13×C16 | C2×C4 | semidirect |
| 26. C2×#6090 | C2×C4 | semidirect |
| 27. C16×D13 | C2×C4 | semidirect |
| 50. C13×C16 | C22×C4 | semidirect |
| 51. #6090 | C22×C4 | semidirect |
| 79. C22×C16 | #261 | semidirect |
| 83. C22×C13 | #367 | semidirect |
| 85. C2×D13 | #367 | semidirect |
| 107. C2×C16 | C2×#261 | semidirect |
| 110. C2×C13 | C2×#367 | semidirect |
| 112. D13 | C2×#367 | semidirect |
| 135. C16 | C22×#261 | semidirect |
| 136. C13 | C22×#367 | semidirect |
| 160. C22 | #11718222 | direct (N × H) |
| 169. C2 | C2×#11718222 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88102 | 2 |
| C2×#11718222 | 2 |
| C22×C16×D13 | 2 |
| C22×#367 | 13 |