Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
378 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22573184 | C2 | semidirect |
| 2. #22562459 | C2 | semidirect |
| 3. #22562245 | C2 | semidirect |
| 4. #22559569 | C2 | semidirect |
| 5. #22558256 | C2 | semidirect |
| 6. #22558171 | C2 | semidirect |
| 7. C67×Q8⋊C16 | C2 | semidirect |
| 95. Q8×C67 | D16 | semidirect |
| 154. Q8⋊C16 | D67 | semidirect |
| 156. C67 | #12328 | semidirect |
| 244. Q8 | D1072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573184 | 2 |
| #22562459 | 2 |
| #22562245 | 2 |
| #22559569 | 2 |
| #22558256 | 2 |
| #22558171 | 2 |
| C67×Q8⋊C16 | 2 |
| #12328 | 67 |