Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
520 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 2. (C2×#261)⋊Q8 | C2 | semidirect |
| 4. #11719071 | C2 | semidirect |
| 5. #11719070 | C2 | semidirect |
| 6. #11719060 | C2 | semidirect |
| 16. C13×#124 | C4 | semidirect |
| 17. #88201 | C4 | semidirect |
| 18. #88190 | C4 | semidirect |
| 19. #88139 | C4 | semidirect |
| 21. #88129 | C4 | semidirect |
| 31. C2×Q8×C13 | C2×C4 | semidirect |
| 42. C2×Dic26 | C2×C4 | semidirect |
| 43. C2×Dic26 | C2×C4 | semidirect |
| 50. C13×C22⋊C4 | C2×C4 | semidirect |
| 51. C42×C13 | C2×C4 | semidirect |
| 52. C22⋊Dic13 | C2×C4 | semidirect |
| 53. #6103 | C2×C4 | semidirect |
| 54. #6103 | C2×C4 | semidirect |
| 55. C4×Dic13 | C2×C4 | semidirect |
| 56. C4×Dic13 | C2×C4 | semidirect |
| 123. #124 | #261 | semidirect |
| 147. C2×Q8 | C2×#261 | semidirect |
| 168. C22⋊C4 | C2×#261 | semidirect |
| 172. C42 | C2×#261 | semidirect |
| 173. C13 | #2379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#124 | 2 |
| (C2×#261)⋊Q8 | 2 |
| #11719150 | 2 |
| #11719071 | 2 |
| #11719070 | 2 |
| #11719060 | 2 |
| #2379 | 13 |