Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
4830 conjugacy classes of subgroups; only the 763 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 763 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. #13113107 | C2 | semidirect |
| 4. #13113106 | C2 | semidirect |
| 5. C13×#1446 | C2 | semidirect |
| 8. C22×Q8×D13 | C4 | semidirect |
| 18. C22×Q8×C13 | C2×C4 | semidirect |
| 30. C22×C4×D13 | Q8 | semidirect |
| 33. C22×Dic26 | C2×C4 | semidirect |
| 50. C22×C4×C13 | C2×Q8 | semidirect |
| 56. C22×Dic13 | C2×Q8 | semidirect |
| 71. #1446 | D13 | direct (N × H) |
| 129. C22×Q8 | C4×D13 | semidirect |
| 147. D13 | #1446 | direct (N × H) |
| 176. C22×C4 | Q8×D13 | semidirect |
| 177. C13 | C2×#1446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×D13 | 2 |
| C2×D13×#95 | 2 |
| #13113107 | 2 |
| #13113106 | 2 |
| C13×#1446 | 2 |
| C2×#1446 | 13 |