Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22562011 | C2 | semidirect |
| 3. #22562006 | C2 | semidirect |
| 4. #22558165 | C2 | semidirect |
| 5. D4⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558163 | C2 | semidirect |
| 7. C67×D4⋊C16 | C2 | semidirect |
| 176. D4⋊C16 | D67 | semidirect |
| 177. C67 | #11632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568916 | 2 |
| #22562011 | 2 |
| #22562006 | 2 |
| #22558165 | 2 |
| D4⋊(C67⋊C16) | 2 |
| #22558163 | 2 |
| C67×D4⋊C16 | 2 |
| #11632 | 67 |