Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#16863234 | C2 | semidirect |
| 2. C2×#16863230 | C2 | semidirect |
| 3. #22562300 | C2 | semidirect |
| 4. #22558408 | C2 | semidirect |
| 5. #22558389 | C2 | semidirect |
| 6. #22558387 | C2 | semidirect |
| 28. C67⋊C32 | D4 | semidirect |
| 103. C67 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863234 | 2 |
| C2×#16863230 | 2 |
| #22562300 | 2 |
| #22558408 | 2 |
| #22558389 | 2 |
| #22558387 | 2 |
| C67×#2215 | 2 |
| #13699 | 67 |