Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
252 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 117 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. D4×#6090 | C2 | semidirect |
| 2. #13112900 | C2 | semidirect |
| 3. D4⋊#6090 | C2 | semidirect |
| 4. #13112754 | C2 | semidirect |
| 33. C13×D8 | C16 | semidirect |
| 55. D4×C13 | C2×C16 | semidirect |
| 66. C8×C13 | C2×C16 | semidirect |
| 108. D8 | #6090 | semidirect |
| 123. C13 | #12062 | semidirect |
| 126. D4 | C2×#6090 | semidirect |
| 137. C8 | C2×#6090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#6090 | 2 |
| #13112900 | 2 |
| D4⋊#6090 | 2 |
| #13112754 | 2 |
| C8×C13×D8 | 2 |
| #12062 | 13 |