Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
482 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16863198 | C2 | semidirect |
| 3. #22561075 | C2 | semidirect |
| 4. #22558301 | C2 | semidirect |
| 5. C2×C4⋊C16×C67 | C2 | semidirect |
| 81. C2×C4×C67 | D16 | semidirect |
| 123. C2×C4⋊C16 | D67 | semidirect |
| 127. C67 | #13448 | semidirect |
| 210. C2×C4 | D1072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1072 | 2 |
| C2×#16863198 | 2 |
| #22561075 | 2 |
| #22558301 | 2 |
| C2×C4⋊C16×C67 | 2 |
| #13448 | 67 |