Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
688 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22568670 | C2 | semidirect |
| 3. #22561880 | C2 | semidirect |
| 4. #22561860 | C2 | semidirect |
| 5. #22558339 | C2 | semidirect |
| 6. #22558329 | C2 | semidirect |
| 7. C67×#1795 | C2 | semidirect |
| 8. C2×#14524068 | C4 | semidirect |
| 9. C22×#11761613 | C4 | semidirect |
| 16. #16863401 | C4 | semidirect |
| 17. #16863392 | C4 | semidirect |
| 31. C22×D268 | C2×C4 | semidirect |
| 38. C2×#11761612 | C2×C4 | semidirect |
| 39. C22×C67⋊C8 | C2×C4 | semidirect |
| 50. #14524002 | C2×C4 | semidirect |
| 263. #1795 | D67 | semidirect |
| 266. C67 | #13102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569477 | 2 |
| #22568670 | 2 |
| #22561880 | 2 |
| #22561860 | 2 |
| #22558339 | 2 |
| #22558329 | 2 |
| C67×#1795 | 2 |
| #13102 | 67 |