Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1538 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 287 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. C4×#88189 | C2 | semidirect |
| 3. #13115249 | C2 | semidirect |
| 4. #13115117 | C2 | semidirect |
| 6. C4×#88074 | C2 | semidirect |
| 16. C22×C4×Dic13 | C22 | semidirect |
| 17. #11718904 | C4 | direct (N × H) |
| 22. C4×C22⋊Dic13 | C22 | semidirect |
| 24. #11718607 | C22 | semidirect |
| 26. #11718604 | C22 | semidirect |
| 28. #11718118 | C22 | semidirect |
| 63. #88189 | C2×C4 | semidirect |
| 70. #88074 | C2×C4 | semidirect |
| 109. C22×Dic13 | C22×C4 | semidirect |
| 123. C22⋊Dic13 | C22×C4 | semidirect |
| 219. C4×C13 | #458 | semidirect |
| 329. C13 | C4×#458 | semidirect |
| 396. C4 | #11718904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718904 | 2 |
| C4×#88189 | 2 |
| #13115249 | 2 |
| #13115117 | 2 |
| #13114784 | 2 |
| C4×#88074 | 2 |
| C4×C13×H(5,𝔽2) | 2 |
| C4×#458 | 13 |