Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
666 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561900 | C2 | semidirect |
| 3. #22561860 | C2 | semidirect |
| 4. #22560179 | C2 | semidirect |
| 5. #22558339 | C2 | semidirect |
| 6. #22558331 | C2 | semidirect |
| 7. C67×#2888 | C2 | semidirect |
| 8. C2×#14524068 | C4 | semidirect |
| 9. C22×#11761613 | C4 | semidirect |
| 17. #16863401 | C4 | semidirect |
| 18. #16863392 | C4 | semidirect |
| 257. #2888 | D67 | semidirect |
| 263. C67 | #13099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569477 | 2 |
| #22561900 | 2 |
| #22561860 | 2 |
| #22560179 | 2 |
| #22558339 | 2 |
| #22558331 | 2 |
| C67×#2888 | 2 |
| #13099 | 67 |