Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
144 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 4. #11718220 | C2 | semidirect |
| 5. #11718219 | C2 | semidirect |
| 14. C13×M32 | C4 | semidirect |
| 15. #88052 | C4 | semidirect |
| 17. C16×D13 | C4 | semidirect |
| 69. M32 | #261 | semidirect |
| 96. C13 | #2155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88103 | 2 |
| #11719092 | 2 |
| D13×M32 | 2 |
| #11718220 | 2 |
| #11718219 | 2 |
| #2155 | 13 |