Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
180 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. Dic67⋊C32 | C2 | semidirect |
| 4. C4×C67⋊C32 | C2 | semidirect |
| 5. C67×#1397 | C2 | semidirect |
| 73. #1397 | D67 | semidirect |
| 75. C67 | #13641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561804 | 2 |
| Dic67⋊C32 | 2 |
| (C2×D67)⋊C32 | 2 |
| C4×C67⋊C32 | 2 |
| C67×#1397 | 2 |
| #13641 | 67 |