Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1010 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 251 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. #13113976 | C2 | direct (N × H) |
| 72. C2×Q8×C13 | Q16 | semidirect |
| 116. Q8×C13 | C2×Q16 | semidirect |
| 206. C2×C13 | #1633 | semidirect |
| 218. C2×Q8 | #6107 | semidirect |
| 247. C13 | C2×#1633 | semidirect |
| 256. Q8 | C2×#6107 | semidirect |
| 286. C2 | #13113976 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718753 | 2 |
| C2×#11718682 | 2 |
| #13113976 | 2 |
| C2×#11718138 | 2 |
| C2×Q8⋊#1055 | 2 |
| C2×Q82×C13 | 2 |
| C2×#1633 | 13 |