Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22558272 | C2 | semidirect |
| 4. Q8⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558125 | C2 | semidirect |
| 7. C67×#2183 | C2 | semidirect |
| 67. C16×C67 | SD16 | semidirect |
| 106. #2183 | D67 | semidirect |
| 113. C67 | #12049 | semidirect |
| 173. C16 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D268 | 2 |
| C8×#11761615 | 2 |
| #22558272 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558163 | 2 |
| #22558125 | 2 |
| C67×#2183 | 2 |
| #12049 | 67 |