Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88124 | C2 | semidirect |
| 3. C13×#423 | C2 | semidirect |
| 5. #11718782 | C2 | semidirect |
| 6. #11718508 | C2 | semidirect |
| 7. #11718490 | C2 | semidirect |
| 79. #423 | D13 | semidirect |
| 142. C13 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6127 | 2 |
| C2×#88124 | 2 |
| C13×#423 | 2 |
| #11718794 | 2 |
| #11718782 | 2 |
| #11718508 | 2 |
| #11718490 | 2 |
| #3080 | 13 |