Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
702 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. C22×#14523962 | C2 | semidirect |
| 3. C2×#16863192 | C2 | semidirect |
| 4. #22558335 | C2 | semidirect |
| 5. C67×#1784 | C2 | semidirect |
| 48. #14523962 | D4 | semidirect |
| 205. C22×C67 | #355 | semidirect |
| 236. #1784 | D67 | semidirect |
| 238. C67 | #13092 | semidirect |
| 443. C22 | #16863192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523962 | 2 |
| #22563863 | 2 |
| C2×#16863192 | 2 |
| #22558335 | 2 |
| C67×#1784 | 2 |
| #13092 | 67 |