Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
704 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#88129 | C2 | semidirect |
| 2. C2×#88129 | C2 | semidirect |
| 4. C2×C4×D52 | C2 | semidirect |
| 5. C4×C13×C4⋊C4 | C2 | semidirect |
| 6. #11718652 | C2 | semidirect |
| 7. #11718600 | C2 | semidirect |
| 8. #11718590 | C2 | semidirect |
| 9. #11718326 | C2 | semidirect |
| 57. C42×C13 | D4 | semidirect |
| 107. C4×C4⋊C4 | D13 | semidirect |
| 190. C42 | D52 | semidirect |
| 191. C13 | #2544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88129 | 2 |
| C2×#88128 | 2 |
| C2×C4×D52 | 2 |
| C4×C13×C4⋊C4 | 2 |
| #11718652 | 2 |
| #11718600 | 2 |
| #11718590 | 2 |
| #11718326 | 2 |
| #2544 | 13 |