Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 15. C13×#106 | C4 | semidirect |
| 16. #88057 | C4 | semidirect |
| 17. #88048 | C4 | semidirect |
| 58. C8×C13 | C4⋊C4 | semidirect |
| 59. #1055 | C4⋊C4 | semidirect |
| 88. #106 | #261 | semidirect |
| 116. C13 | #1944 | semidirect |
| 137. 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 |
| #11719083 | 2 |
| D13×#106 | 2 |
| #11718246 | 2 |
| #1944 | 13 |