Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22561959 | C2 | semidirect |
| 3. #22561958 | C2 | semidirect |
| 4. #22561944 | C2 | semidirect |
| 5. #22560963 | C2 | semidirect |
| 6. #22558288 | C2 | semidirect |
| 7. C67×#2145 | C2 | semidirect |
| 74. #106×C67 | D4 | semidirect |
| 196. #2145 | D67 | semidirect |
| 199. C67 | #13416 | semidirect |
| 263. #106 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570652 | 2 |
| #22561959 | 2 |
| #22561958 | 2 |
| #22561944 | 2 |
| #22560963 | 2 |
| #22558288 | 2 |
| C67×#2145 | 2 |
| #13416 | 67 |