Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16863832 | C2 | semidirect |
| 2. C2×#16863663 | C2 | semidirect |
| 3. #22569881 | C2 | semidirect |
| 4. C2×#16863204 | C2 | semidirect |
| 5. C2×#16863179 | C2 | semidirect |
| 6. #22558317 | C2 | semidirect |
| 7. C2×#357×C67 | C2 | semidirect |
| 60. #14523983 | D4 | semidirect |
| 63. #14523979 | D4 | semidirect |
| 73. C2×D8×C67 | D4 | semidirect |
| 223. C2×#357 | D67 | semidirect |
| 226. C67 | #13307 | semidirect |
| 269. C2×D8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863832 | 2 |
| C2×#16863663 | 2 |
| #22569881 | 2 |
| C2×#16863204 | 2 |
| C2×#16863179 | 2 |
| #22558317 | 2 |
| C2×#357×C67 | 2 |
| #13307 | 67 |