Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #22558192 | C2 | semidirect |
| 5. #22558191 | C2 | semidirect |
| 6. #22558190 | C2 | semidirect |
| 7. C67×#1338 | C2 | semidirect |
| 153. #1338 | D67 | semidirect |
| 154. C67 | #11611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #446×D67 | 2 |
| #22561963 | 2 |
| #22561802 | 2 |
| #22558192 | 2 |
| #22558191 | 2 |
| #22558190 | 2 |
| C67×#1338 | 2 |
| #11611 | 67 |