Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×C13×Q16 | C2 | semidirect |
| 3. C2×#88075 | C2 | semidirect |
| 5. #11718143 | C2 | semidirect |
| 49. C22×D13 | Q16 | semidirect |
| 71. C22×Q16 | D13 | semidirect |
| 135. C13 | #2001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C2×#88200 | 2 |
| C2×#88075 | 2 |
| C2×#88060 | 2 |
| #11718143 | 2 |
| #2001 | 13 |