Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11719538 | C2 | semidirect |
| 2. C2×#88203 | C2 | semidirect |
| 3. C2×#88162 | C2 | semidirect |
| 4. C2×C13×#104 | C2 | semidirect |
| 5. #11718600 | C2 | semidirect |
| 6. C2×#88045 | C2 | semidirect |
| 7. #11718146 | C2 | semidirect |
| 55. C2×D52 | D4 | semidirect |
| 59. C13×M16 | D4 | semidirect |
| 72. #6099 | D4 | semidirect |
| 125. C2×#104 | D13 | semidirect |
| 217. M16 | C22⋊D13 | semidirect |
| 228. C13 | #2006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719538 | 2 |
| C2×#88203 | 2 |
| C2×#88162 | 2 |
| C2×C13×#104 | 2 |
| #11718600 | 2 |
| C2×#88045 | 2 |
| #11718146 | 2 |
| #2006 | 13 |