Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22568173 | C2 | semidirect |
| 4. #22558035 | C2 | semidirect |
| 5. #22558034 | C2 | semidirect |
| 6. #22558031 | C2 | semidirect |
| 85. C4⋊Dic67 | SD16 | semidirect |
| 95. C2×Q8×C67 | SD16 | semidirect |
| 224. C67 | #7748 | semidirect |
| 290. C2×Q8 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568173 | 2 |
| #22561440 | 2 |
| #22561297 | 2 |
| #22558035 | 2 |
| #22558034 | 2 |
| #22558031 | 2 |
| C67×#2014 | 2 |
| #7748 | 67 |