Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 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. #22561925 | C2 | semidirect |
| 4. #22560252 | C2 | semidirect |
| 5. #22558311 | C2 | semidirect |
| 6. #22558310 | C2 | semidirect |
| 7. C67×#2140 | C2 | semidirect |
| 14. #16863646 | C4 | semidirect |
| 43. C2×C67⋊C16 | D4 | semidirect |
| 62. C2×C16×C67 | D4 | semidirect |
| 173. #2140 | D67 | semidirect |
| 177. C67 | #13074 | semidirect |
| 226. 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 |
| #22569853 | 2 |
| #22561925 | 2 |
| #22560252 | 2 |
| #22558311 | 2 |
| #22558310 | 2 |
| C67×#2140 | 2 |
| #13074 | 67 |