Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊(C67⋊C8) | C2 | semidirect |
| 2. #22558985 | C2 | semidirect |
| 5. #22558104 | C2 | semidirect |
| 6. #22558042 | C2 | semidirect |
| 15. #16863142 | C4 | semidirect |
| 16. #16863140 | C4 | semidirect |
| 163. C67 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C67⋊C8) | 2 |
| #22558985 | 2 |
| #22558858 | 2 |
| #22558608 | 2 |
| #22558104 | 2 |
| #22558042 | 2 |
| C67×#1962 | 2 |
| #9577 | 67 |