Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 13. #88102 | C4 | semidirect |
| 14. #88100 | C4 | semidirect |
| 15. C13×#106 | C4 | semidirect |
| 16. #88057 | C4 | semidirect |
| 17. #88048 | C4 | semidirect |
| 56. C8×C13 | C42 | semidirect |
| 57. #1055 | C42 | semidirect |
| 85. #106 | #261 | semidirect |
| 112. C13 | #1776 | semidirect |
| 132. C8 | C4×#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88102 | 2 |
| C2×#88100 | 2 |
| C4⋊C4×#261 | 2 |
| D13×#106 | 2 |
| #11718246 | 2 |
| #1776 | 13 |