Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
604 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 604 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 |
|---|---|---|
| 1. C2×#16863834 | C2 | semidirect |
| 2. #22569818 | C2 | semidirect |
| 3. C2×#16863649 | C2 | semidirect |
| 4. C2×#16863207 | C2 | semidirect |
| 5. #22561926 | C2 | semidirect |
| 6. #22558315 | C2 | semidirect |
| 7. C2×#349×C67 | C2 | semidirect |
| 38. C2×Dic268 | D4 | semidirect |
| 45. C2×D536 | D4 | semidirect |
| 46. C2×D536 | D4 | semidirect |
| 59. #14523977 | D4 | semidirect |
| 62. #14523975 | D4 | semidirect |
| 78. M32×C67 | D4 | semidirect |
| 226. C2×#349 | D67 | semidirect |
| 228. C67 | #13316 | semidirect |
| 292. M32 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863834 | 2 |
| #22569818 | 2 |
| C2×#16863649 | 2 |
| C2×#16863207 | 2 |
| #22561926 | 2 |
| #22558315 | 2 |
| C2×#349×C67 | 2 |
| #13316 | 67 |