Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
272 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 19. #88055 | C4 | semidirect |
| 20. #88048 | C4 | semidirect |
| 21. #88047 | C4 | semidirect |
| 74. #1055 | C42 | semidirect |
| 145. C13 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88055 | 2 |
| C4⋊C4×Dic13 | 2 |
| C2×#88048 | 2 |
| C2×#88047 | 2 |
| C13×#340 | 2 |
| #11718143 | 2 |
| #1776 | 13 |