Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 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. #22561883 | C2 | semidirect |
| 3. #22561862 | C2 | semidirect |
| 5. #22558337 | C2 | semidirect |
| 6. #22558329 | C2 | semidirect |
| 8. C2×#14524073 | C4 | semidirect |
| 9. C22×#11761616 | C4 | semidirect |
| 17. #16863401 | C4 | semidirect |
| 18. #16863392 | C4 | semidirect |
| 31. C22×Dic134 | C2×C4 | semidirect |
| 39. C2×#11761612 | C2×C4 | semidirect |
| 40. C22×C67⋊C8 | C2×C4 | semidirect |
| 48. #14524002 | C2×C4 | semidirect |
| 259. C67 | #13100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569486 | 2 |
| #22561883 | 2 |
| #22561862 | 2 |
| #22560179 | 2 |
| #22558337 | 2 |
| #22558329 | 2 |
| C67×#2883 | 2 |
| #13100 | 67 |