Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22569929 | C2 | semidirect |
| 3. #22569857 | C2 | semidirect |
| 4. C2×#16863210 | C2 | semidirect |
| 5. #22561946 | C2 | semidirect |
| 6. #22558324 | C2 | semidirect |
| 7. C67×#2117 | C2 | semidirect |
| 42. C2×Dic268 | D4 | semidirect |
| 50. C2×D536 | D4 | semidirect |
| 60. #14523979 | D4 | semidirect |
| 78. M32×C67 | D4 | semidirect |
| 217. #2117 | D67 | semidirect |
| 219. C67 | #13310 | semidirect |
| 283. 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 |
| #22569929 | 2 |
| #22569857 | 2 |
| C2×#16863210 | 2 |
| #22561946 | 2 |
| #22558324 | 2 |
| C67×#2117 | 2 |
| #13310 | 67 |