Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1230 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22570605 | C2 | semidirect |
| 3. #22561433 | C2 | semidirect |
| 4. #22561127 | C2 | semidirect |
| 5. #22560167 | C2 | semidirect |
| 6. C4×#14523962 | C2 | semidirect |
| 7. C67×#2567 | C2 | semidirect |
| 188. #2567 | D67 | semidirect |
| 193. C67 | #25871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573980 | 2 |
| #22570605 | 2 |
| #22561433 | 2 |
| #22561127 | 2 |
| #22560167 | 2 |
| C4×#14523962 | 2 |
| C67×#2567 | 2 |
| #25871 | 67 |