Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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×#16863235 | C2 | semidirect |
| 3. #22562300 | C2 | semidirect |
| 4. #22558388 | C2 | semidirect |
| 5. C67×C22⋊C32 | C2 | semidirect |
| 7. C2×Dic536 | C22 | semidirect |
| 13. #16863222 | C22 | semidirect |
| 16. C2×C32×C67 | C22 | semidirect |
| 77. C22×C67 | SD64 | semidirect |
| 98. C22⋊C32 | D67 | semidirect |
| 99. C67 | #13664 | semidirect |
| 108. C2×C32 | C2×D67 | semidirect |
| 175. C22 | #16863235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1072 | 2 |
| C2×#16863235 | 2 |
| #22562300 | 2 |
| #22558388 | 2 |
| C67×C22⋊C32 | 2 |
| #13664 | 67 |