Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
862 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 862 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22561629 | C2 | semidirect |
| 4. #22561361 | C2 | semidirect |
| 5. #22560899 | C2 | semidirect |
| 172. C67 | #29112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568519 | 2 |
| C2×#16863302 | 2 |
| #22561629 | 2 |
| #22561361 | 2 |
| #22560899 | 2 |
| #22560300 | 2 |
| #22560145 | 2 |
| C67×#1749 | 2 |
| #29112 | 67 |