Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×C4×C67⋊C16 | C2 | semidirect |
| 3. #22558172 | C2 | semidirect |
| 4. #22558169 | C2 | semidirect |
| 5. C67×#1568 | C2 | semidirect |
| 140. #1568 | D67 | semidirect |
| 143. C67 | #11673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570779 | 2 |
| C2×C4×C67⋊C16 | 2 |
| #22558172 | 2 |
| #22558169 | 2 |
| C67×#1568 | 2 |
| #11673 | 67 |