Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
220 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 2. #22559603 | C2 | semidirect |
| 4. #22558281 | C2 | semidirect |
| 5. #22558263 | C2 | semidirect |
| 7. Q8×C16×C67 | C2 | semidirect |
| 107. Q8×C16 | D67 | semidirect |
| 113. C67 | #12475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562433 | 2 |
| #22559603 | 2 |
| #22559569 | 2 |
| #22558281 | 2 |
| #22558263 | 2 |
| #22558256 | 2 |
| Q8×C16×C67 | 2 |
| #12475 | 67 |