Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 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. C2×#16863666 | C2 | semidirect |
| 3. #22569879 | C2 | semidirect |
| 4. C2×#16863204 | C2 | semidirect |
| 5. C2×#16863198 | C2 | semidirect |
| 6. #22558318 | C2 | semidirect |
| 7. C2×#350×C67 | C2 | semidirect |
| 48. C2×D536 | D4 | semidirect |
| 60. #14523979 | D4 | semidirect |
| 76. M32×C67 | D4 | semidirect |
| 224. C2×#350 | D67 | semidirect |
| 226. C67 | #13307 | semidirect |
| 288. 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 |
| C2×#16863666 | 2 |
| #22569879 | 2 |
| C2×#16863204 | 2 |
| C2×#16863198 | 2 |
| #22558318 | 2 |
| C2×#350×C67 | 2 |
| #13307 | 67 |