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×#16863837 | C2 | semidirect |
| 3. C2×#16863651 | C2 | semidirect |
| 4. C2×#16863207 | C2 | semidirect |
| 5. C2×#16863177 | C2 | semidirect |
| 6. #22558314 | C2 | semidirect |
| 7. C67×#2141 | C2 | semidirect |
| 60. #14523983 | D4 | semidirect |
| 63. #14523975 | D4 | semidirect |
| 73. C2×Q16×C67 | D4 | semidirect |
| 216. #2141 | D67 | semidirect |
| 219. C67 | #13317 | semidirect |
| 256. C2×Q16 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863837 | 2 |
| #22569819 | 2 |
| C2×#16863651 | 2 |
| C2×#16863207 | 2 |
| C2×#16863177 | 2 |
| #22558314 | 2 |
| C67×#2141 | 2 |
| #13317 | 67 |