Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22573311 | C2 | semidirect |
| 3. #22561937 | C2 | semidirect |
| 4. #22560256 | C2 | semidirect |
| 5. #22558309 | C2 | semidirect |
| 6. #22558308 | C2 | semidirect |
| 7. C67×#2143 | C2 | semidirect |
| 45. C2×C67⋊C16 | D4 | semidirect |
| 67. C2×C16×C67 | D4 | semidirect |
| 184. #2143 | D67 | semidirect |
| 188. C67 | #13076 | semidirect |
| 240. C2×C16 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573311 | 2 |
| #22569867 | 2 |
| #22561937 | 2 |
| #22560256 | 2 |
| #22558309 | 2 |
| #22558308 | 2 |
| C67×#2143 | 2 |
| #13076 | 67 |