Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
594 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22561045 | C2 | semidirect |
| 3. #22560232 | C2 | semidirect |
| 4. #22559987 | C2 | semidirect |
| 5. #22558777 | C2 | semidirect |
| 6. #22558776 | C2 | semidirect |
| 7. C67×#1964 | C2 | semidirect |
| 8. C22×#11761613 | C4 | semidirect |
| 15. C2×#14523976 | C4 | semidirect |
| 17. C2×#14523964 | C4 | semidirect |
| 18. C2×#14523963 | C4 | semidirect |
| 202. C67⋊C8 | #99 | semidirect |
| 246. #1964 | D67 | semidirect |
| 251. C67 | #9785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863630 | 2 |
| #22561045 | 2 |
| #22560232 | 2 |
| #22559987 | 2 |
| #22558777 | 2 |
| #22558776 | 2 |
| C67×#1964 | 2 |
| #9785 | 67 |