Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 21. C13×#103 | C4 | semidirect |
| 22. #88075 | C4 | semidirect |
| 23. #88056 | C4 | semidirect |
| 24. #88050 | C4 | semidirect |
| 131. #103 | #261 | semidirect |
| 174. C13 | #1933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#261)⋊Q8 | 2 |
| C2×#88117 | 2 |
| C2×C8×#261 | 2 |
| #11719083 | 2 |
| D13×#103 | 2 |
| #11718265 | 2 |
| #11718246 | 2 |
| #1933 | 13 |