Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22568797 | C2 | semidirect |
| 3. #22561945 | C2 | semidirect |
| 4. C2×#16863177 | C2 | semidirect |
| 5. #22558311 | C2 | semidirect |
| 6. #22558310 | C2 | semidirect |
| 7. C67×#2145 | C2 | semidirect |
| 12. #16863651 | C4 | semidirect |
| 13. #16863646 | C4 | semidirect |
| 54. #14523975 | C2×C4 | semidirect |
| 55. #14523975 | D4 | semidirect |
| 64. C2×Q16×C67 | C2×C4 | semidirect |
| 66. C2×D8×C67 | C2×C4 | semidirect |
| 73. #106×C67 | D4 | semidirect |
| 196. #2145 | D67 | semidirect |
| 200. C67 | #13008 | semidirect |
| 226. C2×Q16 | C4×D67 | semidirect |
| 228. C2×D8 | C4×D67 | semidirect |
| 264. #106 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569814 | 2 |
| #22568797 | 2 |
| #22561945 | 2 |
| C2×#16863177 | 2 |
| #22558311 | 2 |
| #22558310 | 2 |
| C67×#2145 | 2 |
| #13008 | 67 |