Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
244 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #13116667 | C2 | semidirect |
| 2. D4×#6090 | C2 | semidirect |
| 4. #13112905 | C2 | semidirect |
| 5. #13112792 | C2 | semidirect |
| 6. #13112752 | C2 | semidirect |
| 7. C13×D4⋊C16 | C2 | semidirect |
| 71. #6090 | D8 | semidirect |
| 77. D4⋊C16 | D13 | semidirect |
| 82. D4×C13 | M32 | semidirect |
| 184. C13 | #12038 | semidirect |
| 190. D4 | #88038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13116667 | 2 |
| D4×#6090 | 2 |
| C8×#6104 | 2 |
| #13112905 | 2 |
| #13112792 | 2 |
| #13112752 | 2 |
| C13×D4⋊C16 | 2 |
| #12038 | 13 |