Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
444 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22569194 | C2 | semidirect |
| 3. #22558841 | C2 | semidirect |
| 4. #22558550 | C2 | semidirect |
| 5. C67⋊#1308 | C2 | semidirect |
| 6. #22558081 | C2 | semidirect |
| 7. C67×#1490 | C2 | semidirect |
| 208. #1490 | D67 | semidirect |
| 212. C67 | #9532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570347 | 2 |
| #22569194 | 2 |
| #22558841 | 2 |
| #22558550 | 2 |
| C67⋊#1308 | 2 |
| #22558081 | 2 |
| C67×#1490 | 2 |
| #9532 | 67 |