Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #11719100 | C2 | semidirect |
| 4. M16×#261 | C2 | semidirect |
| 6. #11718274 | C2 | semidirect |
| 7. #11718272 | C2 | semidirect |
| 23. C13×#101 | C4 | semidirect |
| 24. #88076 | C4 | semidirect |
| 25. #88063 | C4 | semidirect |
| 26. #88063 | C4 | semidirect |
| 122. #101 | #261 | semidirect |
| 163. C13 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719155 | 2 |
| C2×#88118 | 2 |
| #11719100 | 2 |
| M16×#261 | 2 |
| #11718412 | 2 |
| #11718274 | 2 |
| #11718272 | 2 |
| #1932 | 13 |