Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
7118 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.
This group has 7118 conjugacy classes of subgroups — too many to draw. Only its 1459 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×#11718892 | C2 | direct (N × H) |
| 3. C22×#88071 | C2 | semidirect |
| 4. C24×Q8×C13 | C2 | semidirect |
| 7. C23×Q8×C13 | C22 | semidirect |
| 12. #11718892 | C22 | direct (N × H) |
| 13. C2×#88071 | C22 | semidirect |
| 17. C24×D13 | Q8 | semidirect |
| 21. C22×Q8×C13 | C23 | semidirect |
| 30. #88071 | C23 | semidirect |
| 41. C23×D13 | C2×Q8 | semidirect |
| 54. C24×Q8 | D13 | semidirect |
| 71. C22×D13 | C22×Q8 | semidirect |
| 81. C23×Q8 | C2×D13 | semidirect |
| 88. C22×C13 | #393 | semidirect |
| 108. C22×Q8 | C22×D13 | semidirect |
| 118. C2×C13 | C2×#393 | semidirect |
| 145. C13 | C22×#393 | semidirect |
| 171. C22 | #11718892 | direct (N × H) |
| 181. C2 | C2×#11718892 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6103 | 2 |
| C2×#11718892 | 2 |
| C22×#88071 | 2 |
| C24×Q8×C13 | 2 |
| C22×#393 | 13 |