Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
800 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22561186 | C2 | semidirect |
| 3. #22561037 | C2 | semidirect |
| 4. #22558946 | C2 | semidirect |
| 5. #22558944 | C2 | semidirect |
| 6. #22558942 | C2 | semidirect |
| 7. C67×#1962 | C2 | semidirect |
| 8. #16864140 | C4 | semidirect |
| 244. #1962 | D67 | semidirect |
| 248. C67 | #8532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574607 | 2 |
| #22561186 | 2 |
| #22561037 | 2 |
| #22558946 | 2 |
| #22558944 | 2 |
| #22558942 | 2 |
| C67×#1962 | 2 |
| #8532 | 67 |